Gromov-Witten invariants of stable maps with fields

Abstract

We construct the Gromov-Witten invariants of moduli of stable morphisms to $\Pf$ with fields. This is the all genus mathematical theory of the Guffin-Sharpe-Witten model, and is a modified twisted Gromov-Witten invariants of $\Pf$. These invariants are constructed using the cosection localization of Kiem-Li, an algebro-geometric analogue of Witten's perturbed equations in Landau-Ginzburg theory. We prove that these invariants coincide, up to sign, with the Gromov-Witten invariants of quintics.

33 pages

References in corpus (7)

• Phases of $N=2$ Theories In Two Dimensions
• The moduli space of stable quotients
• Landau-Ginzburg/Calabi-Yau correspondence for quintic three-folds via symplectic transformations
• The Witten equation and its virtual fundamental cycle
• A-twisted Landau-Ginzburg models
• Gromov-Witten invariants of varieties with holomorphic 2-forms
• Derived Kodaira Spencer map, Cosection lemma, and semiregularity

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• Congruences on K-theoretic Gromov--Witten invariants
• Relative Resolution and Its Applications
• The Moduli of Sections Has a Canonical Obstruction Theory
• Quantum Lefschetz without curves
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