#### Conference abstracts

Session A2 - Computational Algebraic Geometry

July 10, 18:00 ~ 18:25

## The Chow form of a reciprocal linear space

### Cynthia Vinzant

### North Carolina State University, USA - clvinzan@ncsu.edu

A reciprocal linear space is the image of a linear space under coordinate-wise inversion. This nice algebraic variety appears in many contexts and its structure is governed by the combinatorics of the underlying hyperplane arrangement. A reciprocal linear space is also an example of a hyperbolic variety, meaning that there is a family of linear spaces all of whose intersections with it are real. This special real structure is witnessed by a determinantal representation of its Chow form in the Grassmannian. In this talk, I will introduce reciprocal linear spaces and discuss the relation of their algebraic properties to their combinatorial and real structure.

Joint work with Mario Kummer (Max Planck Institute, Leipzig, Germany).