Geometry & Topology

Standard versus reduced genus-one Gromov–Witten invariants

Aleksey Zinger

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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.

Article information

Geom. Topol., Volume 12, Number 2 (2008), 1203-1241.

Received: 3 August 2007
Revised: 17 January 2008
Accepted: 27 February 2008
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35] 53D99: None of the above, but in this section

Gromov–Witten invariants mirror symmetry


Zinger, Aleksey. Standard versus reduced genus-one Gromov–Witten invariants. Geom. Topol. 12 (2008), no. 2, 1203--1241. doi:10.2140/gt.2008.12.1203.

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