Standard versus reduced genus-one Gromov–Witten invariants

By A. Zinger. 2007

55 citations recorded by the source corpus.

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. 14D20, 14N35; 53D45, 53D99

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/22ab965b874aa82bfdd4ba314b2362cd251c81a9

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In Geometry and Topology

Citations in the corpus

Landau–Ginzburg/Calabi–Yau correspondence for quintic three-folds via symplectic transformations (2008, methodology): “single invariant and when one needs to eﬀectively compute the full higher genus Gromov–Witten theory. The genus-one theory has been computed only recently by A. Zinger after a great deal of hard work [Zi08]. Computations in higher genera are out of mathematicians’ reach for the moment. There is a ph”
The reduced genus 1 Gromov-Witten invariants of Calabi-Yau hypersurfaces (2007, background): “scendant classes are involved. 8 The terms on the second line above arise from the last term in the formula of Theorem 2. In the n=3,4,5 cases, the latter is GW0;X 1,k(d;1) −GW X 1,k(d;1). We show in [Z5] that this is the case for all n. For n=6, Theorem 2 would then give X∞ d=1 edTGWX 1,0(d;1) = − ”
Logarithmic Stable Maps (2008, background): “The hyperplane section principle for reduced genus 1 Gromov-Witten invariants and the comparisons between reduced and standard genus 1 invariants are accomplished in [23, 35, 36, 37 ].”