Counting curves on surfaces in Calabi-Yau 3-folds

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.

11 pages. Published version

References in corpus (4)

• A Farey Tail for Attractor Black Holes
• Donaldson-Thomas invariants via microlocal geometry
• The M5-Brane Elliptic Genus: Modularity and BPS States
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Cited by in corpus (6)

• Curve counting and S-duality
• Crystal Melting, BPS Quivers and Plethystics
• Scaling Black Holes and Modularity
• Flops and the S-duality conjecture
• Generalized Donaldson-Thomas Invariants of 2-Dimensional sheaves on local P^2
• Hilbert Schemes, Donaldson-Thomas Theory, Vafa-Witten and Seiberg Witten theories