Big quantum cohomology of even dimensional intersections of two quadrics

Xiaowen Hu

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arXiv · 2109.11469

Big quantum cohomology of even dimensional intersections of two quadrics

Xiaowen Hu

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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.

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Xiaowen Hu. 2021-09-23. Big quantum cohomology of even dimensional intersections of two quadrics. https://arxiv.org/abs/2109.11469

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