Abstract
We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or skew-symmetric form. We establish Pieri rules for the classical cohomology and the small quantum cohomology ring of these varieties, which give a combinatorial formula for the product of any Schubert class with certain special Schubert classes. We also give presentations of these rings, with integer coefficients, in terms of special Schubert class generators and relations.
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The authors were supported in part by NSF Grant DMS-0603822 (Buch), the Swiss National Science Foundation (Kresch), and NSF Grants DMS-0401082 and DMS-0639033 (Tamvakis).
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Buch, A.S., Kresch, A. & Tamvakis, H. Quantum Pieri rules for isotropic Grassmannians. Invent. math. 178, 345–405 (2009). https://doi.org/10.1007/s00222-009-0201-y
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DOI: https://doi.org/10.1007/s00222-009-0201-y