Gregory Berhuy and Zinovy Reichstein: On the notion of canonical dimension for algebraic groups,

Submission: 2004, Jun 18

We define and study a numerical invariant of an algebraic group action which we call the canonical dimension. As an application of the resulting theory we give estimates on the minimal number of parameters required to define a projective generic hypersurface of degree d.

2000 Mathematics Subject Classification: 11E72, 14L30, 14J70

Keywords and Phrases: algebraic group, G-variety, generic splitting field, essential dimension, canonical dimension, homogeneous forms

Full text: dvi.gz 69 k, dvi 164 k, ps.gz 768 k, pdf.gz 325 k, pdf 358 k.

Server Home Page