Skip to main content

Stringy invariants for horospherical varieties of complexity one

Langlois, Kevin, Pech, Clelia, Raibaut, Michel (2015) Stringy invariants for horospherical varieties of complexity one. arXiv preprint, . (Submitted) (doi:arXiv:1511.03852v1)

Abstract

In this paper we determine the stringy motivic volume of log terminal horospherical G-varieties of complexity one, where G is a connected reductive linear algebraic group. The stringy motivic volume of a log terminal variety is an invariant of singularities which was introduced by Batyrev and plays an important role in mirror symmetry for Calabi-Yau varieties. A horospherical G-variety of complexity one is a normal G-variety which is equivariantly birational to a product C×G/H, where C is a smooth projective curve and the closed subgroup H contains a maximal unipotent subgroup of G. The simplest example of such a variety is a normal surface with a non-trivial ?*-action. Our formula extends the results of Batyrev-Moreau [BM13] on stringy invariants of horospherical embeddings. The proof involves the study of the arc space of a horospherical variety of complexity one and a combinatorial description of its orbits. In contrast to [BM13], the number of orbits is no longer countable, which adds significant difficulties to the problem. As a corollary of our main theorem, we obtain a smoothness criterion using a comparison of the stringy and usual Euler characteristics.

Item Type: Article
DOI/Identification number: arXiv:1511.03852v1
Subjects: Q Science > QA Mathematics (inc Computing science) > QA171 Representation theory
Q Science > QA Mathematics (inc Computing science) > QA564 Algebraic Geometry
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Clelia Pech
Date Deposited: 12 Sep 2016 10:16 UTC
Last Modified: 20 Jun 2019 10:43 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/57218 (The current URI for this page, for reference purposes)
Pech, Clelia: https://orcid.org/0000-0001-6142-6679
  • Depositors only (login required):

Downloads

Downloads per month over past year