Standard versus reduced genus-one Gromov–Witten invariants

Zinger, Aleksey

doi:10.2140/gt.2008.12.1203

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Standard versus reduced genus-one Gromov–Witten invariants

Aleksey Zinger

Geometry & 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 2000

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

Volume 12, issue 2 (2008)