Hassett-Tschinkel correspondence: Modality and projective hypersurfaces

JOURNAL OF ALGEBRA

卷:348

Article

Arzhantsev, Ivan V.¹  Sharoyko, Elena V.¹ 

[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Dept Higher Algebra, Moscow 119991, Russia

关键词: Unipotent group;    Local algebra;    Modality;    Projective quadric;   

DOI  :  10.1016/j.jalgebra.2011.09.026

来源: Elsevier

【 摘 要 】

In 1999, B. Hassett and Yu. Tschinkel introduced a remarkable correspondence between generically transitive actions of the commutative unipotent algebraic group G(a)(n) and finite-dimensional local algebras. In this paper we develop Hassett-Tschinkel correspondence and calculate modality of generically transitive (G(a)(n)-actions on projective spaces, classify actions of modality one, and characterize generically transitive G(a)(n)-actions on projective hypersurfaces of given degree. In particular, actions on degenerate projective quadrics are studied. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free