Wall-crossing formula and genus-one Virasoro conjecture for Fano complete intersections

Abstract

The Virasoro conjecture predicts a set of universal relations among all genera Gromov--Witten invariants of any smooth projective variety. The conjecture is well understood for semisimple theories, but remains largely open in the non-semisimple setting. We prove the genus-one Virasoro conjecture on the ambient state space of smooth Fano complete intersections in projective space. For most of these complete intersections, the big quantum cohomology is nowhere semisimple. We also generalize the wall-crossing formula for quasimap invariants with weighted markings to the equivariant twisted setting, allowing descendant insertions at light markings. Together with genus-one quantum Lefschetz for quasimaps with light markings, this wall-crossing formula provides the key bridge from the Gromov--Witten theory of the complete intersection to the semisimple equivariant twisted theory of the projective space.