Higher genus relative and orbifold Gromov-Witten invariants

Hsian-Hua Tseng Ohio State University Fenglong You University of Alberta

Algebraic Geometry mathscidoc:1907.01003

Geometry & Topology
Given a smooth projective variety X and a smooth divisor D\subset X. We study relative Gromov-Witten invariants of (X,D) and the corresponding orbifold Gromov-Witten invariants of the r-th root stack X_{D,r}. For sufficiently large r, we prove that orbifold Gromov- Witten invariants of X_{D,r} are polynomials in r. Moreover, higher genus relative Gromov-Witten invariants of (X,D) are exactly the constant terms of the corresponding higher genus orbifold Gromov-Witten invari- ants of X_{D,r}. We also provide a new proof for the equality between genus zero relative and orbifold Gromov-Witten invariants, originally proved by Abramovich-Cadman-Wise. When r is sufficiently large and X=C is a curve, we prove that stationary relative invariants of C are equal to the stationary orbifold invariants in all genera.
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  • to appear in Geometry & Topology
@inproceedings{hsian-huahigher,
  title={Higher genus relative and orbifold Gromov-Witten invariants},
  author={Hsian-Hua Tseng, and Fenglong You},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190702223601524414393},
  booktitle={Geometry & Topology},
}
Hsian-Hua Tseng, and Fenglong You. Higher genus relative and orbifold Gromov-Witten invariants. In Geometry & Topology. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190702223601524414393.
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