Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties
TLDR
In this article, the authors introduce a method of constructing the virtual cycle of any scheme associated with a tangent-obstruction complex and apply this method to construct the virtual moduli cycle of the moduli of stable maps from n-pointed genus g curves to any smooth projective variety.Abstract:
We introduce a method of constructing the virtual cycle of any scheme associated with a tangent-obstruction complex. We apply this method to constructing the virtual moduli cycle of the moduli of stable maps from n-pointed genus g curves to any smooth projective variety. As an application, we give an algebraic definition of GW-invariants for any smooth projective variety.read more
Citations
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Localization of virtual classes
T. Graber,Rahul Pandharipande +1 more
TL;DR: In this paper, the authors prove a localization formula for virtual fundamental classes in the context of torus equivariant perfect obstruction theories, where the higher genus Gromov-Witten invariants of projective space are expressed as graph sums of tautological integrals over moduli spaces of stable pointed curves.
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Gromov-Witten theory and Donaldson-Thomas theory, I
TL;DR: In this paper, the Gromov-Witten/Donaldson-Thomas correspondence for 3-folds in both the absolute and relative cases was discussed. And degree 0 formulas were proved for both the relative and absolute versions of the theory for toric varieties.
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Hodge integrals and Gromov-Witten theory
Carel Faber,Rahul Pandharipande +1 more
TL;DR: In this article, a universal system of differential equations is proposed to determine the generating function of the Chern classes of the Hodge bundle in Gromov-Witten theory for any target X. The genus g, degree d multiple cover contribution of a rational curve is found to be simply proportional to the Euler characteristic of M_g.
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Gromov-Witten theory of Deligne-Mumford stacks
TL;DR: In this article, Gromov-Witten invariants of a smooth complex Deligne-Mumford stack with a projective coarse moduli space were introduced and proved.
References
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TL;DR: In this article, the authors implique l'accord avec les conditions generales d'utilisation (http://www.numdam.org/legal.php).
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Intersection theory on the moduli space of curves and the matrix Airy function
TL;DR: In this article, it was shown that two natural approaches to quantum gravity coincide, relying on the equivalence of each approach to KdV equations, and they also investigated related mathematical problems.