# Counting curves with fixed j-invariant

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Yoav Len

created by risa on 20 Nov 2015

26 nov 2015
-- 14:00

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

**Abstract.**

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.