Higher genus relative and orbifold Gromov–Witten invariants

Tseng, Hsian-Hua¹ ; You, Fenglong²

¹Department of Mathematics, Ohio State University, Columbus, OH, United States
²Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada

Geometry & topology, Tome 24 (2020) no. 6, pp. 2749-2779

Résumé

Given a smooth projective variety X and a smooth divisor D ⊂ X, we study relative Gromov–Witten invariants of (X,D) and the corresponding orbifold Gromov–Witten invariants of the r th root stack XD,r. For sufficiently large r, we prove that orbifold Gromov–Witten invariants of XD,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 invariants of XD,r. We also provide a new proof for the equality between genus-zero relative and orbifold Gromov–Witten invariants, originally proved by Abramovich, Cadman and Wise (2017). 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.

Détail

Classification : 14N35, 14H10
Keywords: relative Gromov–Witten invariants, root stacks, degeneration, virtual localization

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