| Autor: |
Silversmith, Rob |
| Předmět: |
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| Zdroj: |
Transactions of the American Mathematical Society; Sep2023, Vol. 376 Issue 9, p6573-6622, 50p |
| Abstrakt: |
We give a graph-sum algorithm that expresses any genus-g Gromov-Witten invariant of the symmetric product orbifold \operatorname {Sym}^d\mathbb {P}^r≔ [(\mathbb {P}^r)^d/S_d] in terms of "Hurwitz-Hodge integrals" – integrals over (compactified) Hurwitz spaces. We apply the algorithm to prove a mirror-type theorem for \operatorname {Sym}^d\mathbb {P}^r in genus zero. The theorem states that a generating function of Gromov-Witten invariants of \operatorname {Sym}^d\mathbb {P}^r is equal to an explicit power series I_{\operatorname {Sym}^d\mathbb {P}^r}, conditional upon a conjectural combinatorial identity. This is a first step in the direction of proving Ruan's Crepant Resolution Conjecture for the resolution Hilb^{(d)}(\mathbb {P}^2) of the coarse moduli space of \operatorname {Sym}^d\mathbb {P}^2. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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