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      On the rigidity of stable maps to Calabi-Yau threefolds

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          Abstract

          If X is a nonsingular curve in a Calabi--Yau threefold Y whose normal bundle N_{X/Y} is a generic semistable bundle, are the local Gromov-Witten invariants of X well defined? For X of genus two or higher, the issues are subtle. We will formulate a precise line of inquiry and present some results, some positive and some negative.

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          Hodge integrals and degenerate contributions

          R. Pandharipande (1998)
          Degenerate contributions to higher genus Gromov-Witten invariants of Calabi-Yau 3-folds are computed via Hodge integrals. The vanishing of contributions of covers of elliptic curves conjectured by Gopakumar and Vafa is proven. A formula for degree 1 covers for all genus pairs is computed in agreement with M-theoretic calculations of Gopakumar and Vafa. Finally, these results lead to a proof of a formula in the tautological ring of the moduli space of curves previously conjectured by Faber.
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            Publication date Created: 11 May 2004
            Publication date Updated: 2009-03-13
            Article
            DOI: 10.2140/gtm.2006.8.97
            ArXiV ID: math/0405204
            SO-VID: af9248b9-01a7-4ae2-be90-b7ce75e37cc1
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            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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            ACM classes 14J32, 14N35
            Journal reference Geom. Topol. Monogr. 8 (2006) 97-104
            Comments This is the version published by Geometry & Topology Monographs on 22 April 2006
            Categories math.AG

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