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Seminari de Geometria Algebraica 2025/2026 |
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Conferenciant
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Títol |
Data i hora |
Valentina Beorchia
Università di Trieste
Contact:
miro@ub.edu
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Variations of hyperplane section and weak Lefschetz property of complete intersections
In 1998 Harris, Mazur and Pandharipande posed the following question: does the family of all smooth hyperplane sections of a smooth
irreducible projective hypersurface vary maximally in moduli? As observed by Beauville in 2025, the question is equivalent to the
weak Lefschetz property of the Jacobian ideal in the hypersurface degree. We translate the problem into the vanishing of the cohomology
of a suitable stable syzygy bundle. We give a positive answer in sufficiently high degree, by using Grauert-Mülich's theorem and Flenner's
restriction theorem. Joint work with R. M. Mirò-Roig.
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Divendres 10 d'octubre, 15h10, Aula IMUB
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Guillem Blanco
Universitat Politècnica de Catalunya
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The Gauss-Manin system of an ICIS
The Gauss-Manin system of an isolated hypersurface singularity is a classical example of a regular holonomic
D-module carrying a Hodge filtration. Its relevance comes from the connection with the local Bernstein-Sato
polynomial, the monodromy, and the spectrum of the singularity. In this talk, we will define the Gauss-Manin
system of an isolated complete intersection singularity (ICIS) and study its Hodge filtration using deformation
theory and local cohomology modules. In particular, we will relate the Hodge filtration to a generalized Brieskorn
lattice. Moreover, using recent results on rational and Du Bois singularities, we will recover the microlocal
structure and the link with b-functions, generalizing the hypersurface case.
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Divendres 17 d'octubre, 15h10, Aula T2
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Andrés Rojas
Universitat de Barcelona
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Hurwitz-Brill-Noether, K3 surfaces and stability conditions
Whereas the geometry of Brill-Noether loci for general curves is described by a collection of theorems dating back to the 70s and 80s,
Brill-Noether theory for curves of a fixed gonality \(k\) has not been understood until recent times. I will explain how, by using
Bridgeland stability on K3 surfaces with an elliptic pencil, one can find the first known examples of \(k\)-gonal curves which behave
generically from this “Hurwitz-Brill-Noether” perspective, establishing a parallel to Lazarsfeld’s remarkable proof of the Gieseker-Petri
theorem. Joint work with G. Farkas and S. Feyzbakhsh.
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Divendres 24 d'octubre, 15h10, Aula T2
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Binggang Qu
ICMAT, Madrid
Contact:
sombra@ub.edu
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Arakelov geometry on flag varieties over function fields, and related topics
Let \(k\) be an algebraically closed field of characteristic zero. Let \(C/k\) be a projective smooth curve with function field \(K = k(C)\).
Let \(G/k\) be a reductive group and \(F \longrightarrow C\) be a principal \(G\)-bundle. Let \(P\) be a parabolic subgroup of
\(G\) and \(\lambda : P \longrightarrow \mathbb{G}_m\) be a strictly anti-dominant character. Then \(F/P\) is a \(G/P\)-bundle on \(C\),
on which we have a natural line bundle \(L_\lambda := F \times_P k_\lambda\) that induces a height function \(h_{L_\lambda}\).
We compute Arakelov-theoretic invariants (the height filtration, the successive minima and the Boucksom-Chen concave transform of
\(h_{L_\lambda}\)) and algebro-geometric invariants (the stable base locus of \(L_\lambda\), the movable cones of \(F/P\)) in terms of the stability of \(F\).
Joint work with Yangyu Fan and Wenbin Luo.
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Divendres 31 d'octubre, 15h10, Aula T2
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Irene Spelta
Humboldt-Universität zu Berlin
Contact:
jcnaranjo@ub.edu
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Automorphisms of Jacobians and unlikely intersections
The study of abelian varieties with non-trivial endomorphism algebras is a classical topic in algebraic geometry. A fundamental result by Shimura classifies all families of principally polarized abelian varieties whose endomorphism algebras properly contain \(\mathbb{Z}\). However, a complete analogous classification for Jacobians remains open and unlikely phenomena frequently occur. In this talk, we focus on the unlikely intersections described by certain families of Jacobians arising from unramified cyclic coverings of hyperelliptic curves. This is joint work with J. C. Naranjo, P. Pirola, and A. Ortega.
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Divendres 7 de novembre, 15h10, Aula T2
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M. Casanellas
P. Macias Marques
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Jornada de jóvenes doctores en geometría algebraica III
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13 - 14 de novembre, FMI-UB
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Valerio Toledano Laredo
Northeastern University
Contact:
marta.mazzocco@upc.edu
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A Riemann-Hilbert correspondence for q-difference equations in several variables
A Riemann-Hilbert correspondence for Fuchsian q-difference equations in one variable was obtained by Birkhoff in 1913, and elegantly recast as an equivalence of categories by Sauloy in 2003. We propose a definition of regular singularities in several variables and obtain the classification of the corresponding q-difference equations in terms of elliptic monodromy data. Our results are valid when the coefficient group is an arbitrary linear algebraic group, and the step lattice a discrete cocompact subgroup of \((\mathbb{C}^*)^n\).
This is joint work with Julien Roques (U. Lyon 1).
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Dimarts 25 de novembre, 15h10, Aula IMUB
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Víctor Valdebenito
Universidad de La Frontera
Contact:
jcnaranjo@ub.edu
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Prym-Tyurin varieties coming from intermediate coverings of curves with action group
It is well-known that the study of the moduli space of principally polarized abelian varieties in low dimensions can be approached through Jacobian and Prym varieties arising from smooth projective curves. However, for dimensions higher than five, no similar construction in terms of curves is known. In this talk, we present a new construction of such varieties in any dimension, obtained from intermediate coverings of curves endowed with a group action. Specifically, we introduce a new method to produce principally polarized subvarieties of Jacobian varieties with prime exponent.
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Divendres 12 de desembre, 15h10, Aula T2
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Jieao Song
Università degli Studi di Milano
Contact:
andresrojas@ub.edu
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Projective models of hyperkähler manifolds and Coble type hypersurfaces
Hyperkähler manifolds are natural generalizations of K3 surfaces in higher dimensions. Geometric descriptions for locally complete families of projective hyperkähler manifolds are only known in very few cases. In this talk, we first describe the projective geometry of the Hilbert square of a K3 surface of genus 7 or 8, by making use of the Mukai model: in both cases, it can be realized as a degeneracy locus on an ambient homogeneous space. From this, we deduce a geometric description for the two locally complete families of K3\(^{[2]}\)-type (square 4 and square 6 with divisibility 1), in terms of Coble type hypersurfaces. Based on a joint work with Ángel Ríos Ortiz and Andrés Rojas, and an ongoing work also with Benedetta Piroddi.
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Divendres 23 de gener, 15h10, Aula T2
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Jungkai Chen
National Taiwan University
Contact:
miguel.angel.barja@upc.edu
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Irregular varieties with small volume in dimension three and higher
For varieties of general type, it is essential to investigate the distribution of their birational invariants. The Noether-Severi inequality in dimension three asserts that vol(X) is greater than or equal to 4/3 times of Euler characteristic of canonical sheaf.
In this talk, we are going to present some recent progress on refined version of Noether-Severi inequality as well as the lower bound of canonical volume. We will also illustrate its connection with slope inequality, and Noether inequality for varieties of general type in general.
This talk is based on a joint work in progress with Yong Hu, Zhi Jiang, and Tong Zhang.
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Divendres 30 de gener, Sessió doble, 15h10, Aula T2
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Paolo Stellari
Università degli Studi di Milano
Contact:
marti.lahoz@ub.edu
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Weakly approximable triangulated categories: the interplay between
metrics and higher categories
We review some recently developed techniques that allow us to describe in an intrinsic way the classical triangulated subcategories of a weakly approximable triangulated category. We then explain how the theory of (excellent) metrics plays a crucial role in the study of higher categorical enhancements of such subcategories. The focus is on examples of geometric and algebraic nature. The new results are joint work with Alberto Canonaco and Amnon Neeman.
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Divendres 30 de gener, Sessió doble, 16h20, Aula T2
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I. Barros
J.I. Burgos
S. Casalaina-Martin
F. Fité
O. de Gaay Fortman
G. van der Geer
S. Grushevsky
A. Iribar López
T. Krämer
E. Markman
B. Moonen
A. Ortega
I. Spelta
A. Verra
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Abelian varieties and their moduli
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3 - 6 de febrer, Aula B5, FMI-UB
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Alberto Fernández Boix
Universitat Politècnica de Catalunya
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Regularity of deficiency modules through spectral sequences
The goal of this talk is to obtain upper bounds for the regularity of graded deficiency modules in the spirit of the one obtained by Kummini–Murai in the monomial case building upon the spectral sequence formalism developed by Alvarez Montaner, Boix and Zarzuela. This spectral sequence formalism allows us not only to recover Kummini–Murai’s upper bound for monomial ideals, but also to extend it for other types of rings, which include toric face rings and some binomial edge rings, producing to the best of our knowledge new upper bounds for the regularity of graded deficiency modules of this type of rings. The content of this talk is based on joint work with Santiago Zarzuela.
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Divendres 13 de febrer, 15h10, Aula T2
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Leonardo Roa Leguizamon
CIMAT
Contact:
costa@ub.edu
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Stability conditions for coherent systems on curves
Bridgeland's notion of stability conditions on triangulated categories provides a new set of tools to study moduli spaces. In this talk, I will present stability conditions for the category of coherent systems on an integral curve. I will define a three-parameter family of pre-stability conditions on its derived category using tilting, and then investigate when these conditions qualify as stability conditions. Additionally, I will examine the semistability of specific objects under these conditions, namely torsion, free, and complete tilted systems, without relying on the support property.
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Divendres 20 de febrer, 15h10, Aula T2
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Miguel Ángel Barja
Universitat Politècnica de Catalunya
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Asymptotic methods, stability conditions and the slope of fibred varieties over surfaces
Given a fibration \(f: X\to S\) over a surface \(S\), and a line bundle \(L\) on \(X\), we will propose and study a definition for the slope of \(L\) with respect to \(f\), using stability conditions on \(S\). This construction is a natural generalization of previously known slopes of fibrations over curves and points, and is coherent with asymptotic constructions such as Frobenius limits. Then we will give slope inequalities for this situation in the cases where \(X\) is a variety of maximal Albanese dimension or \(X\) is a 3-fold. This is a joint work in progress with Martí Lahoz and Andrés Rojas.
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Divendres 6 de març, 15h10, Aula T2
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Uli Walther
Purdue University
Contact:
josep.alvarez@upc.edu
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What is a logarithmic comparison theorem?
The talk will answer the title question and the origins of the notion, discuss historic examples of increasing complexity, and lead up to a recent update to a 25 year old conjecture regarding the interplay of LCT's and certain vector fields. Why the conjecture was updated will be discussed next, in form of a theorem, found jointly with Abraham del Valle Rodriguez and Daniel Bath; it establishes consequences of LCT beyond the scope of the original conjecture.
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Divendres 13 de març, 15h10, Aula T2
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Martín Sombra
Universitat de Barcelona
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Kähler-Einstein toric submanifolds of the projective space
After the seminal work of E. Calabi and S.-S. Chern, it is conjectured that the Kähler-Einstein submanifolds of a projective space equipped with the Fubini-Study metric are homogeneous spaces. This conjecture has been proven for submanifolds of codimension at most 2, but is widely open in the general case. I will explain an approach aiming to prove this conjecture for toric manifolds of arbitrary codimension. This is joint work with Antonio Di Scala (Politecnico di Torino).
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Divendres 20 de març, 15h10, Aula T2
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Farhad Babaee
University of Bristol
Contact:
roberto.gualdi@upc.edu
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Divendres 10 d'abril, 15h10, Aula T2
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G. Alfarano
R. Homs
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Gröbner free methods and their applications
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13 - 15 d'abril, Aula IC, FMI-UB
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Teresa Krick
Universidad de Buenos Aires
Contact:
cdandrea@ub.edu
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Un positivstellensatz efectivo sobre los números racionales para conjuntos semialgebraicos finitos
Presentaré resultados sobre la representación exacta de un polinomio racional (multivariado) que es no-negativo sobre un conjunto semialgebraico finito como suma de cuadrados de polinomios racionales. Mostraré la existencia de tal representación en el caso estrictamente positivo y una condición suficiente para el caso no-negativo, conjuntamente con cotas de grado y altura (tamaño bit) para la representación.
Trabajo en colaboración con Lorenzo Baldi, U. Leipzig, y Bernard Mourrain, INRIA.
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Divendres 17 d'abril, 15h10, Aula T2
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Lidia Stoppino
Università di Pavia
Contact:
miguel.angel.barja@upc.edu
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Divendres 8 de maig, 15h10, Aula T2
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Meng Chen
Fudan University
Contact:
miguel.angel.barja@upc.edu
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Divendres 15 de maig, 15h10, Aula T2
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Federico Moretti
Stony Brook University
Contact:
andresrojas@ub.edu
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Divendres 22 de maig, 15h10, Aula T2
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Divendres 29 de maig, 15h10, Aula T2
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Divendres 5 de juny, 15h10, Aula T2
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Divendres 12 de juny, 15h10, Aula T2
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Divendres 19 de juny, 15h10, Aula T2
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