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The Crepant Resolution Conjecture for 3-dimensional flags modulo an involution
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In this article, the genus zero Gromov-Witten potential function of a crepant resolution Y of the quotient scheme F / Z_2, after setting a quantum parameter to -1, making a linear change of variables, and analytically continuing coefficients, is checked.Abstract:
After fixing a non-degenerate bilinear form on a vector space V we define an involution of the manifold of flags F in V by taking a flag to its orthogonal complement. When V is of dimension 3 we check that the Crepant Resolution Conjecture of J. Bryan and T. Graber holds: the genus zero (orbifold) Gromov-Witten potential function of [F / Z_2] agrees (up to unstable terms) with the genus zero Gromov-Witten potential function of a crepant resolution Y of the quotient scheme F / Z_2, after setting a quantum parameter to -1, making a linear change of variables, and analytically continuing coefficients. The crepant resolution Y (a hypersurface in the Hilbert scheme Hilb^2 P^2) is the projectivization of a novel rank 2 vector bundle over P^2.read more
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Journal Article
The Crepant Resolution Conjecture
Jim Bryan,Tom Graver +1 more
TL;DR: For the Gromov-Witten theory of the orbifold, this article proved a conjectural equivalence between the equivariant and the resolution, and proved the equivalence for the equivariant Gromkov-witten theories of Sym^n C^2 and Hilb c^2.
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Wall-Crossings in Toric Gromov-Witten Theory II: Local Examples
TL;DR: In this article, the Coates-Corti-Iritani-Tseng/Ruan form of the Crepant Resolution Conjecture was analyzed for the case of crepant partial resolutions.
Journal ArticleDOI
On the Crepant Resolution Conjecture in the Local Case
TL;DR: In this paper, the Coates-Iritani-Tseng/Ruan form of the Crepant Resolution Conjecture was analyzed for local Calabi-Yau 3-folds.
Journal ArticleDOI
On the Crepant Resolution Conjecture in the Local Case
TL;DR: In this paper, the Coates-Corti-Iritani-Tseng/Ruan form of the Crepant Resolution Conjecture was analyzed for local Calabi-Yau 3-folds.
Posted Content
On the mathematics and physics of high genus invariants of [C^3/Z_3]
Vincent Bouchard,Renzo Cavalieri +1 more
TL;DR: In this paper, the Gromov-Witten invariants of [C^3/Z_3] in arbitrary genus and the mathematical framework for expressing these invariants as Hodge integrals are presented.
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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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A New Cohomology Theory of Orbifold
TL;DR: In this paper, a new cohomology ring for almost complex orbifolds is constructed based on the string theory model in physics, and the key theorem is the associativity of this new ring.
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Gromov-Witten theory of Deligne-Mumford stacks
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