On the structure of certain natural cones over moduli spaces of genus-one holomorphic maps

• Autores: Aleksey Zinger
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 214, Nº 2, 2007, págs. 878-933
• Idioma: inglés
• DOI: 10.1016/j.aim.2007.03.009
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• Resumen

  • 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.