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Counting Elliptic Curves in K3 Surfaces

Junho Lee·Naichung Conan Leung
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Abstract

We compute the genus one family Gromov-Witten invariants of K3 surfaces for non-primitive classes. These calculations verify Gottsche-Yau-Zaslow formula for non-primitive classes with index two. Our approach is to use the genus two topological recursion formula and the symplectic sum formula to establish relationships among various generating functions.

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Junho Lee, Naichung Conan Leung. 2004-05-03. Counting Elliptic Curves in K3 Surfaces. https://arxiv.org/abs/math/0405041

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