Li–Zinger formula for reduced Gromov–Witten invariants of quintics

Let QP4Q\subset\mathbb{P}^4 be a smooth quintic, and let Ng,d(Q)N_{g,d}(Q) denote its genus gg, degree dd Gromov–Witten invariant. Let Nh,d(Q)N'_{h,d}(Q) be the reduced invariant defined by the modular Euler class construction for d>2g2d>2g-2. Li–Zinger conjecture. There are universal constants chc_h such that, for all d>2g2d>2g-2,

Ng,d(Q)=0hgchNh,d(Q).N_{g,d}(Q)=\sum_{0\leq h\leq g}c_hN'_{h,d}(Q).

This conjecture predicts a universal relation between ordinary and reduced Gromov–Witten invariants of quintic threefolds. The supplied text gives no resolution status.

Sources & referencesView supporting material

Primary source

Yi Hu, “Relative Resolution and Its Applications”, arXiv:1310.2237 (2013).

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