Reduced genus-one gromov-witten invariants

Aleksey Zinger Stanford University

Differential Geometry mathscidoc:1609.10145

Journal of Differential Geometry, 83, (2), 407-460, 2009
In a previous paper, we described a natural closed subset, M 0 1,k(X,A; J), of the moduli space M1,k(X,A; J) of stable genusone J-holomorphic maps into a symplectic manifold X. In this paper we generalize the definition of the main component to moduli spaces of perturbed, in a restricted way, J-holomorphic maps and conclude that M 0 1,k(X,A; J), just like M1,k(X,A; J), carries a virtual fundamental class, which can be used to define symplectic invariants. These truly genus-one invariants constitute part of the standard genus-one Gromov-Witten invariants, which arise from the entire moduli space M1,k(X,A; J). The new invariants are more geometric and can be used to compute the genus-one GW-invariants of complete intersections, as shown in a separate paper.
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@inproceedings{aleksey2009reduced,
  title={REDUCED GENUS-ONE GROMOV-WITTEN INVARIANTS},
  author={Aleksey Zinger},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911202430523968802},
  booktitle={Journal of Differential Geometry},
  volume={83},
  number={2},
  pages={407-460},
  year={2009},
}
Aleksey Zinger. REDUCED GENUS-ONE GROMOV-WITTEN INVARIANTS. 2009. Vol. 83. In Journal of Differential Geometry. pp.407-460. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911202430523968802.
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