Big quantum cohomology of even dimensional intersections of two quadrics
arXiv:2109.11469
Abstract
For even dimensional smooth complete intersections, of dimension at least 4, of two quadric hypersurfaces in a projective space, we study the genus zero Gromov-Witten invariants by the monodromy group of its whole family. We compute the invariants of length 4 and 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 solving a curve counting problem. We show that the generating function of genus zero Gromov-Witten invariants has a positive radius of convergence. We show that, although the small quantum cohomology is not semisimple, the associated Frobenius manifold is generically tame semisimple.
60 pages. Minor changes. Typos corrected. References updated. The relevant Macaulay2 packages can be found at https://github.com/huxw06/Quantum-cohomology-of-Fano-complete-intersections. Comments are welcome!