Open Access
Translator Disclaimer
2007 Del Pezzo surfaces and representation theory
Vera Serganova, Alexei Skorobogatov
Algebra Number Theory 1(4): 393-419 (2007). DOI: 10.2140/ant.2007.1.393


The connection between del Pezzo surfaces and root systems goes back to Coxeter and Du Val, and was given modern treatment by Manin in his seminal book Cubic forms. Batyrev conjectured that a universal torsor on a del Pezzo surface can be embedded into a certain projective homogeneous space of the semisimple group with the same root system, equivariantly with respect to the maximal torus action. Computational proofs of this conjecture based on the structure of the Cox ring have been given recently by Popov and Derenthal. We give a new proof of Batyrev’s conjecture using an inductive process, interpreting the blowing-up of a point on a del Pezzo surface in terms of representations of Lie algebras corresponding to Hermitian symmetric pairs.


Download Citation

Vera Serganova. Alexei Skorobogatov. "Del Pezzo surfaces and representation theory." Algebra Number Theory 1 (4) 393 - 419, 2007.


Received: 2 February 2007; Revised: 11 August 2007; Accepted: 15 September 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1170.14026
MathSciNet: MR2368955
Digital Object Identifier: 10.2140/ant.2007.1.393

Primary: 14J26
Secondary: 17B10 , 17B25

Keywords: del Pezzo surface , homogeneous space , Lie algebra

Rights: Copyright © 2007 Mathematical Sciences Publishers


Vol.1 • No. 4 • 2007
Back to Top