Hassett-Tschinkel correspondence: Modality and projective hypersurfaces

Details Hassett-Tschinkel correspondence: Modality and projective hypersurfaces Hassett-Tschinkel correspondence: Modality and projective hypersurfaces

2009-12-08

arxiv.org/abs/0912.1474v3

Journal of Algebra 348 (2011), no. 1, 217-232

Mathematics

Algebraic Geometry

minor corrections, 18 pages

Scientific paper

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

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