Counting curves on surfaces in CalabiYau 3folds
Abstract
Motivated by Sduality modularity conjectures in string theory, we define new invariants counting a restricted class of 2dimensional torsion sheaves, enumerating pairs $Z\subset H$ in a CalabiYau threefold X. Here H is a member of a sufficiently positive linear system and Z is a 1dimensional subscheme of it. The associated sheaf is the ideal sheaf of $Z\subset H$, pushed forward to X and considered as a certain JoyceSong pair in the derived category of X. We express these invariants in terms of the MNOP invariants of X.
 Publication:

arXiv eprints
 Pub Date:
 August 2013
 arXiv:
 arXiv:1309.0051
 Bibcode:
 2013arXiv1309.0051G
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory
 EPrint:
 11 pages. Published version