Geometry Seminar

 

University of Tor Vergata, Department of Mathematics

21st of January 2025, 14:30-16:00, room D’Antoni

 

 

 

 

 

 

 

A logarithmic approach to linear series

 

Francesca Carocci

Tor Vergata

 

 

 

 

Maps to projective space are given by basepoint-free linear series, thus these are key to understanding the extrinsic geometry of algebraic curves. How does a linear series degenerate when the underlying curve degenerates and becomes nodal? Eisenbud and Harris gave a satisfactory answer to this question when the nodal curve is of compact type. I will report on a joint work in progress with Luca Battistella and Jonathan Wise, in which we review this question from a moduli-theoretic and logarithmic perspective. The logarithmic prospective helps understanding the rich polyhedral and combinatorial structures underlying degenerations of linear series; these are linked with the theory of matroids and Bruhat–Tits buildings.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This talk is part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry