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arXiv · 1309.0051

Counting curves on surfaces in Calabi-Yau 3-folds

Amin Gholampour·Artan Sheshmani·R. P. Thomas
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Abstract

Motivated by S-duality modularity conjectures in string theory, we define new invariants counting a restricted class of 2-dimensional torsion sheaves, enumerating pairs $Z\subset H$ in a Calabi-Yau threefold X. Here H is a member of a sufficiently positive linear system and Z is a 1-dimensional subscheme of it. The associated sheaf is the ideal sheaf of $Z\subset H$, pushed forward to X and considered as a certain Joyce-Song pair in the derived category of X. We express these invariants in terms of the MNOP invariants of X.

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Amin Gholampour, Artan Sheshmani, R. P. Thomas. 2013-08-31. Counting curves on surfaces in Calabi-Yau 3-folds. https://doi.org/10.1007/s00208-014-1035-5

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