Sum Formulas for Local Gromov-Witten Invariants of Spin Curves
Junho Lee
TL;DR
This paper develops sum formulas for local Gromov-Witten invariants of spin curves, connecting them to invariants of ruled surfaces and confirming recent conjectures by Maulik and Pandharipande.
Contribution
It introduces a method to derive sum formulas for local GW invariants of spin curves from known formulas for ruled surfaces, verifying recent conjectures.
Findings
Sum formulas for local Gromov-Witten invariants of spin curves derived.
Verification of Maulik-Pandharipande formulas.
Connection established between local GW invariants and ruled surface invariants.
Abstract
Holomorphic 2-forms on K\"{a}hler surfaces lead to "Local Gromov-Witten invariants" of spin curves. This paper shows how to derive sum formulas for such local GW invariants from the sum formula for GW invariants of certain ruled surfaces. These sum formulas also verify the Maulik-Pandharipande formulas that were recently proved by Kiem and Li.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Advanced Algebra and Geometry