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arxiv: math/0405204 · v2 · submitted 2004-05-11 · 🧮 math.AG

On the rigidity of stable maps to Calabi-Yau threefolds

classification 🧮 math.AG
keywords somebundlecalabi--yaucalabi-yaucurvedefinedformulategeneric
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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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