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Geometry of horospherical varieties of Picard rank one

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)

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
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)

University of Kent Author Information

Pech, Clelia.

Creator's ORCID: https://orcid.org/0000-0001-6142-6679
CReDIT Contributor Roles:

Perrin, Nigel.

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