Big quantum cohomology of even dimensional intersections of two quadrics
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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2021
- DOI:
- 10.48550/arXiv.2109.11469
- arXiv:
- arXiv:2109.11469
- Bibcode:
- 2021arXiv210911469H
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Symplectic Geometry;
- 14N35;
- 53D45
- E-Print:
- 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!