Remarks on gluing punctured logarithmic maps
Mark Gross
TL;DR
This paper develops a general gluing formula for punctured stable log maps, extending existing log Gromov-Witten invariants techniques and applying it to mirror symmetry for K3 surfaces.
Contribution
It introduces a broad gluing formalism for punctured stable log maps, simplifying and generalizing previous formulas in the field.
Findings
Unified gluing formula for log Gromov-Witten invariants.
Simplification of Li-Ruan, Jun Li, and Kim-Lho-Ruddat formulas.
Application to canonical wall structures for K3 surfaces.
Abstract
We consider some well-behaved cases of the gluing formalism for punctured stable log maps of Abramovich-Chen-Gross-Siebert. This gives a gluing formula for log Gromov-Witten invariants in a diverse set of cases; in particular, the gluing formulae of Li-Ruan, Jun Li and Kim-Lho-Ruddat become an easy special case. The last section gives an application of this gluing formalism to canonical wall structures for K3 surfaces as constructed by Gross and Siebert in "The canonical wall structure and intrinsic mirror symmetry."
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology