On the genus-one gromov-witten invariants of complete intersections

Jun Li Stanford University Aleksey Zinger Stanford University

Differential Geometry mathscidoc:1609.10129

Journal of Differential Geometry, 82, (3), 641-690, 2009
We state and prove a long-elusive relation between genus-one Gromov-Witten of a complete intersection and twisted Gromov Witten invariants of the ambient projective space. As shown in a previous paper, certain naturally arising cones of holomorphic vector bundle sections over the main component M 0 1,k(Pn, d) of the moduli space of stable genus-one holomorphic maps into Pn have a well-defined euler class. In this paper, we extend this result to moduli spaces of perturbed, in a restricted way, J-holomorphic maps. This extension is used to show that these cones are the correct genus-one analogues of the vector bundles relating genuszero Gromov-Witten invariants of a complete intersection to those of the ambient projective space. A relationship for higher-genus invariants is conjectured as well.
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@inproceedings{jun2009on,
  title={ON THE GENUS-ONE GROMOV-WITTEN INVARIANTS OF COMPLETE INTERSECTIONS},
  author={Jun Li, and Aleksey Zinger},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911194231282782786},
  booktitle={Journal of Differential Geometry},
  volume={82},
  number={3},
  pages={641-690},
  year={2009},
}
Jun Li, and Aleksey Zinger. ON THE GENUS-ONE GROMOV-WITTEN INVARIANTS OF COMPLETE INTERSECTIONS. 2009. Vol. 82. In Journal of Differential Geometry. pp.641-690. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911194231282782786.
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