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Tropical Count of Curves on Abelian Varieties
Lars Halvard Halle, Simon Rose
We investigate the problem of counting tropical genus g curves in g-dimensional tropical abelian varieties. For g = 2, 3, we prove that the tropical count matches the count provide…
Introduction to Gromov-Witten Theory
Simon Rose
The goal of these notes is to provide an informal introduction to Gromov-Witten theory with an emphasis on its role in counting curves in surfaces. These notes are based on a talk…
Elliptic Calabi-Yau threefolds over a del Pezzo surface
Simon Rose, Noriko Yui
We consider certain elliptic threefolds over the projective plane (more generally over certain rational surfaces) with a section in Weierstrass normal form. In particular, over a d…
Counting Hyperelliptic curves on Abelian surfaces with Quasi-modular forms
Simon Rose
In this paper we produce a generating function for the number of hyperelliptic curves (up to translation) on a polarized Abelian surfaces using the crepant resolution conjecture an…