Computing genus zero Gromov–Witten invariants of Fano varieties

Abstract

a b s t r a c tWe present a recursive algorithm computing all the genus zero Gromov-Witten invariants from a finite number of initial ones, for Fano manifolds with generically semisimple quantum (and tame semisimple small quantum) (p, p)-type cohomology, whose first Chern class is a strictly positive combination of effective integral basic divisors.

Embedding pointed curves in K3 surfaces

“…Remark. Semi-simplicity allows us to reconstruct the full quantum cohomology even without assuming that the ordinary cohomology is generated by H 2 , see [BM04] and [Mas11]. (The case where the cohomology is generated by H 2 is addressed in [KM94].)…”