On the structure of certain natural cones over moduli spaces of genus-one holomorphic maps |
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Authors: | Aleksey Zinger |
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Institution: | Department of Mathematics, Stanford University, Stanford, CA 94305-2125, USA |
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Abstract: | We show that certain naturally arising cones over the main component of a moduli space of J0-holomorphic maps into Pn have a well-defined Euler class. We also prove that this is the case if the standard complex structure J0 on Pn is replaced by a nearby almost complex structure J. The genus-zero analogue of the cone considered in this paper is a vector bundle. The genus-zero Gromov-Witten invariant of a projective complete intersection can be viewed as the Euler class of such a vector bundle. As shown in a separate paper, this is also the case for the “genus-one part” of the genus-one GW-invariant. The remaining part is a multiple of the genus-zero GW-invariant. |
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Keywords: | Moduli spaces of stable maps Gromov-Witten invariants Pushforward sheaf |
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