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The intrinsic normal cone
Kai Behrend,Barbara Fantechi +1 more
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In this paper, a construction of virtual fundamental classes of certain types of moduli spaces is proposed, where the fundamental classes can be expressed as a set of classes of modulus spaces.Abstract:
We suggest a construction of virtual fundamental classes of certain types of moduli spaces.read more
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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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Notes on stable maps and quantum cohomology
W. Fulton,Rahul Pandharipande +1 more
TL;DR: In this article, the authors present notes from a jointly taught class at the University of Chicago and lectures by the first author in Santa Cruz, discussing moduli spaces of stable maps, Gromov-Witten invariants, quantum cohomology, and examples.
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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 invariants and quantization of quadratic hamiltonians
TL;DR: In this article, a formalism based on quantization of quadratichamil tonians and loop groups is proposed, which provides a convenient home for most known general results and conjectures about Gromov-Witten invariants of compact symplectic manifolds and Frobenius structures at higher genus.
References
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The irreducibility of the space of curves of given genus
Pierre Deligne,David Mumford +1 more
TL;DR: In this article, the authors implique l'accord avec les conditions generales d'utilisation (http://www.numdam.org/legal.php).
Book
Algebraic Geometry: A First Course
TL;DR: In this article, the authors introduce the notion of Tangent Spaces to Grassmannians and describe the relationship between them and regular functions and maps. But they do not discuss their application in the context of dimension computations.
Journal ArticleDOI
Functors of Artin rings
TL;DR: In this article, Grothendieck showed that a covariant functor F from C to Sets is pro-representable if it has the form 1.0, 2.0.