Higher genus Gromov–Witten invariants as genus zero invariants of symmetric products

By K. Costello. 2003

91 citations recorded by the source corpus.

I prove a formula expressing the descendent genus g Gromov-Witten invariants of a projective variety X in terms of genus 0 invariants of its symmetric product stack Sg+1(X). When X is a point, the latter are structure constants of the symmetric group, and we obtain a new way of calculating the Gromov- Witten invariants of a point.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/74082b2f7157dfb26d34110fb2ac414a2e615f49

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

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Citations in the corpus

Expanded Degenerations and Pairs (2011, methodology): “This relies on Costello’s formalism of labeling by a set [13], applied to expanded degenerations.”
Orbifold techniques in degeneration formulas (2011, unknown): “(γi) Y j∈Mν γj +(X,D) Γν Proof. This follows from the projection formula. ♣ 4.8.7. An auxiliary stack of expansions. We prove Proposition 4.8.5 by applying the main technical result, Theorem 5.0.1 of [Co]. This needs some preparation. Let T ′ be the stack deﬁned as follows. T ′(S) = {D × S ⊂ X →εν X”
Decomposition of degenerate Gromov–Witten invariants (2017, unknown): “cartesian diagram M ˝(X 0=b 0;) / M m˝ (X 0=b 0;) M ˝(X 0=b 0;0) /M m ˝ (X 0=b 0; 0) (2)The morphism : a ˝ : m˝=m M ˝(X 0=b 0; 0) ! M m(X 0=b 0; 0) is of pure degree 1 in the sense of Costello [Cos06]. 32 DAN ABRAMOVICH, QILE CHEN, MARK GROSS, AND BERND SIEBERT Proof. (1) Both the Aut(~˝)-invarian”
Comparison theorems for Gromov–Witten invariants of smooth pairs and of degenerations (2012, methodology): “The technique has also been used in [18, 2, 6, 9, 15].”