Gromov-Witten invariants of varieties with holomorphic 2-forms

Abstract

We show that a holomorphic two-form $\theta$ on a smooth algebraic variety X localizes the virtual fundamental class of the moduli of stable maps $\mgn(X,β)$ to the locus where $\theta$ degenerates; it then enables us to define the localized GW-invariant, an algebro-geometric analogue of the local invariant of Lee and Parker in symplectic geometry, which coincides with the ordinary GW-invariant when X is proper. It is deformation invariant. Using this, we prove formulas for low degree GW-invariants of minimal general type surfaces with p_g>0 conjectured by Maulik and Pandharipande.

36 pages

References in corpus (1)

• Donaldson-Thomas invariants via microlocal geometry

Cited by in corpus (6)

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• Localizing Virtual Cycles by Cosections
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• Derived Kodaira Spencer map, Cosection lemma, and semiregularity
• 1-point Gromov-Witten invariants of the moduli spaces of sheaves over the projective plane
• Donaldson Thomas invariant of P^1 scroll