Big quantum cohomology of even dimensional intersections of two quadrics

Xiaowen Hu

Published 2021-09-23Version 1

For every even dimensional smooth complete intersection, of dimension at least 4, of two quadric hypersurfaces in a projective space, we compute the genus zero Gromov-Witten invariants of length 4, and then we show that, besides a special invariant, all genus zero Gromov-Witten invariants can be reconstructed from the invariants of length 4. In dimension 4, we compute the special invariant by relating it to a curve counting problem. We also show that the generating function of genus zero Gromov-Witten invariants has a positive radius of convergence, and the associated Frobenius manifold is generically semisimple.