On the Structure of Certain Natural Cones over Moduli Spaces of Genus-One Holomorphic Maps

2004/06/06 by Aleksey Zinger, Zinger, Aleksey
Mathematics · #14N35 #53D99 #Commutative Algebra (math.AC) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.AC #math.SG #msc:14N35 #msc:53D99

paper · pdf · doi:10.48550/arxiv.math/0406104

an error corrected; 45 pages, 3 figures

arxiv created 2005/07/05 · arxiv updated 2009/12/01

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 always a vector bundle. The genus-zero Gromov-Witten invariant of a projective hypersurface is 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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