 |
|
Seminari de Geometria Algebraica 2025/2026 |
|
| |
|
Conferenciant
|
Títol |
Data i hora |
Valentina Beorchia
Università di Trieste
Contact:
miro@ub.edu
|
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.
|
Divendres 10 d'octubre, 15h10, Aula IMUB
|
Guillem Blanco
Universitat Politècnica de Catalunya
|
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.
|
Divendres 17 d'octubre, 15h10, Aula T2
|
Andrés Rojas
Universitat de Barcelona
|
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.
|
Divendres 24 d'octubre, 15h10, Aula T2
|
Binggang Qu
ICMAT, Madrid
Contact:
sombra@ub.edu
|
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.
|
Divendres 31 d'octubre, 15h10, Aula T2
|
Irene Spelta
Humboldt-Universität zu Berlin
Contact:
jcnaranjo@ub.edu
|
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.
|
Divendres 7 de novembre, 15h10, Aula T2
|
M. Casanellas
P. Macias Marques
|
Jornada de jóvenes doctores en geometría algebraica III
|
13 - 14 de novembre, FMI-UB
|
Valerio Toledano Laredo
Northeastern University
Contact:
marta.mazzocco@upc.edu
|
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).
|
Dimarts 25 de novembre, 15h10, Aula IMUB
|
Víctor Valdebenito
Universidad de La Frontera
Contact:
jcnaranjo@ub.edu
|
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.
|
Divendres 12 de desembre, 15h10, Aula T2
|
Jieao Song
Università degli Studi di Milano
Contact:
andresrojas@ub.edu
|
|
Divendres 23 de gener, 15h10, Aula T2
|
Jungkai Chen
National Taiwan University
Contact:
miguel.angel.barja@upc.edu
|
|
Divendres 30 de gener, 15h10, Aula T2
|
I. Barros
J.I. Burgos
S. Casalaina-Martin
F. Fité
G. van der Geer
S. Grushevsky
A. Iribar López
T. Krämer
E. Markman
B. Moonen
A. Ortega
R. Salvati Manni
I. Spelta
A. Verra
C. Voisin
U. Zannier
|
Abelian varieties and their moduli
|
3 - 6 de febrer, Aula T1, FMI-UB
|
|
|
Divendres 13 de febrer, 15h10, Aula IMUB
|
|
|
Divendres 20 de febrer, 15h10, Aula IMUB
|
|
|
Divendres 27 de febrer, 15h10, Aula IMUB
|
|
|
Divendres 6 de març, 15h10, Aula IMUB
|
|
|
Divendres 13 de març, 15h10, Aula IMUB
|
|
|
Divendres 20 de març, 15h10, Aula IMUB
|
|
|
Divendres 10 d'abril, 15h10, Aula IMUB
|
|
|
Divendres 17 d'abril, 15h10, Aula IMUB
|
|
|
Divendres 8 de maig, 15h10, Aula IMUB
|
Meng Chen
Fudan University
Contact:
miguel.angel.barja@upc.edu
|
|
Divendres 15 de maig, 15h10, Aula IMUB
|
|
|
Divendres 22 de maig, 15h10, Aula IMUB
|
|
|
Divendres 29 de maig, 15h10, Aula IMUB
|
|
|
Divendres 5 de juny, 15h10, Aula IMUB
|
|
|
Divendres 12 de juny, 15h10, Aula IMUB
|
|
|
Divendres 19 de juny, 15h10, Aula IMUB
|
|
