Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Counting curves with fixed j-invariant

Yoav Len

created by risa on 20 Nov 2015

26 nov 2015 -- 14:00

Aula 211, Dip. Matematica, Università "Roma Tre", Roma


I will discuss a correspondence between the number of algebraic and tropical elliptic curves on toric surfaces with fixed j-invariant. The proof combines ideas from tropical geometry with recent tools from log geometry. As an application, we obtain a new enumerative formula for Hirzerbruch surfaces, relating the number of such curves with the number of rational curves having mild tangency with the boundary. In addition, I will show how the correspondence theorem is used to recover Pandharipande's formula for the projective plane. This is joint work with Dhruv Ranganathan.

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