Counting curves on surfaces in Calabi-Yau 3-folds

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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.
OriginalsprogEngelsk
TidsskriftMathematische Annalen
Vol/bind360
Nummer1
ISSN0025-5831
DOI
StatusUdgivet - 31 aug. 2013
Eksternt udgivetJa

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  • math.AG, hep-th

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