Geometry Seminar

 

University of Tor Vergata, Department of Mathematics

4th of February 2025, 14:30-16:00,room D’Antoni

 

 

 

 

 

 

 

A short proof of the multiple cover formula

 

Thomas Blomme

Université de Genève

 

 

 

 

Enumerating genus g curves passing through g points in an abelian surface is a natural problem, whose difficulty highly depends on the degree of the curves. For "primitive" degrees, we have an easy explicit answer. For "divisible" classes, such a resolution is quite demanding and often out of reach. Yet, the invariants for divisible classes easily express in terms of the invariants for primitive classes through the multiple cover formula, conjectured by G. Oberdieck a few years ago. In this talk, we'll show how tropical geometry enables to prove the formula without any kind of concrete enumeration.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This talk is part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry and Prin PNRR 2022 Mathematical Primitives for Post Quantum Digital Signatures