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arXiv · 1701.06596

Counting Curves on a Weierstrass Model

Francois Greer
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Abstract

Let $X\to \mathbb P^2$ be the elliptic Calabi-Yau threefold given by a general Weierstrass equation. We answer the enumerative question of how many discrete rational curves lie over lines in the base, proving part of a conjecture by Huang, Katz, and Klemm. The key inputs are a modularity theorem of Kudla and Millson for locally symmetric spaces of orthogonal type and the deformation theory of $A_n$ singularities.

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Francois Greer. 2017-01-23. Counting Curves on a Weierstrass Model. https://arxiv.org/abs/1701.06596

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