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Tropical gluing formulae for Gromov-Witten invariants

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arxiv 1703.05433 v1 pith:X5PRPRLX submitted 2017-03-16 math.SG math.AGmath.DG

Tropical gluing formulae for Gromov-Witten invariants

classification math.SG math.AGmath.DG
keywords gromov-witteninvariantsformulaformulaegluingtropicalgeneralizesaxioms
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We prove two tropical gluing formulae for Gromov-Witten invariants of exploded manifolds, useful for calculating Gromov-Witten invariants of a symplectic manifold using a normal-crossing degeneration. The first formula generalizes the symplectic-sum formula for Gromov-Witten invariants. The second formula is stronger, and also generalizes Kontsevich and Manin's splitting and genus-reduction axioms. Both tropical gluing formulae have versions incorporating gravitational descendants.

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  1. The integral Chow ring of $\mathscr{M}_{0}(\mathbb{P}^r, 2)$

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    The integral Chow ring of M_0(P^r, 2) is presented as a quotient of a three-variable polynomial ring with all non-trivial relations encoded by two rational generating functions.