Del Pezzo surfaces and representation theory

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

In his book "Cubic forms" Manin discovered that del Pezzo surfaces are related to root systems. To explain the many numerical coincidences Batyrev conjectured that a universal torsor on a del Pezzo surface can be embedded in a certain projective homogeneous space of the semisimple group with the same root system, equivariantly with respect to the maximal torus action. We prove this conjecture for del Pezzo surfaces of degrees greater than 1. Our proof uses an inductive process based on representations of Lie algebras corresponding to Hermitian symmetric pairs.
revised version, 26 pages, to appear in J. Algebra and Number Theory

Keywords

Algebraic Geometry, Representation Theory

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/161921

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0611737
 http://arxiv.org/abs/math/0611737
 J. Algebra and Number Theory 1 (2007) 393-419.

Collections

arXiv