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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060

Standard versus reduced genus-one Gromov–Witten invariants

Aleksey Zinger

Geometry and Topology 12 (2008) 1203–1241

DOI: 10.2140/gt.2008.12.1203

Abstract

We give an explicit formula for the difference between the standard and reduced genus-one Gromov–Witten invariants. Combined with previous work on geometric properties of the latter, this paper makes it possible to compute the standard genus-one GW-invariants of complete intersections. In particular, we obtain a closed formula for the genus-one GW-invariants of a Calabi–Yau projective hypersurface and verify a recent mirror symmetry prediction for a sextic fourfold as a special case.

Keywords

Gromov–Witten invariants, mirror symmetry

Mathematical Subject Classification

Primary: 14D20, 14N35

Secondary: 53D45, 53D99

References
Publication

Received: 3 August 2007
Revised: 17 January 2008
Accepted: 27 February 2008
Published: 25 May 2008
Proposed: Jim Bryan
Seconded: Yasha Eliashberg, Gang Tian

Authors
Aleksey Zinger
Department of Mathematics
SUNY Stony Brook
Stony Brook, NY 11794-3651
USA
http://www.math.sunysb.edu/~azinger