Gonzales, Rafael, Pech, Clelia, Perrin, Nigel, Samokhin, A (2021) Geometry of horospherical varieties of Picard rank one. International Mathematics Research Notices, . ISSN 1073-7928. E-ISSN 1687-0247. (doi:10.1093/imrn/rnaa331) (KAR id:83827)
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Official URL: https://doi.org/10.1093/imrn/rnaa331 |
Abstract
We study the geometry of smooth non-homogeneous horospherical varieties of Picard rank one. These have been classified by Pasquier and include the well-known odd symplectic Grassmannians. We focus our study on quantum cohomology, with a view towards Dubrovin’s conjecture. In particular, we describe the cohomology groups of these varieties as well as a Chevalley formula, and prove that many Gromov-Witten invariants are enumerative. This enables us to prove that in many cases the quantum cohomology is semisimple. We give a presentation of the quantum cohomology ring for odd symplectic Grassmannians. The final two sections are devoted to the derived categories of coherent sheaves on horospherical varieties. We first discuss a general construction of exceptional bundles on these varieties. We then study in detail the case of the horospherical variety associated to the exceptional group G2, and construct a full rectangular Lefschetz exceptional collection in the derived category.
Item Type: | Article |
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DOI/Identification number: | 10.1093/imrn/rnaa331 |
Subjects: | Q Science > QA Mathematics (inc Computing science) > QA150 Algebra |
Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | Clelia Pech |
Date Deposited: | 30 Oct 2020 16:32 UTC |
Last Modified: | 23 Feb 2022 00:00 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/83827 (The current URI for this page, for reference purposes) |
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