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Standard versus reduced genus-one Gromov–Witten
invariants
Aleksey Zinger
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Geometry and Topology 12 (2008)
1203–1241
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Abstract
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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.
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Keywords
Gromov–Witten invariants, mirror
symmetry
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Mathematical Subject Classification
Primary: 14D20, 14N35
Secondary: 53D45, 53D99
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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
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