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On the notion of canonical dimension for algebraic groups (in special volume in honor of Michael Artin: part I)

On the notion of canonical dimension for algebraic groups (in special volume in honor of Michael Artin: part I)
On the notion of canonical dimension for algebraic groups (in special volume in honor of Michael Artin: part I)
We define and study a numerical invariant of an algebraic group action which we call the canonical dimension. We then apply the resulting theory to the problem of computing the minimal number of parameters required to define a generic hypersurface of degree d in pn-1.
algebraic group, g-variety, generic splitting field, essential dimension, canonical dimension, homogeneous forms
0001-8708
128-171
Berhuy, Grégory
3d8146f6-19cf-411b-92a2-cd0c2129ec73
Reichstein, Zinovy
d74abee7-a010-460e-8695-6a727b423a56
Berhuy, Grégory
3d8146f6-19cf-411b-92a2-cd0c2129ec73
Reichstein, Zinovy
d74abee7-a010-460e-8695-6a727b423a56

Berhuy, Grégory and Reichstein, Zinovy (2005) On the notion of canonical dimension for algebraic groups (in special volume in honor of Michael Artin: part I). Advances in Mathematics, 198 (1), 128-171. (doi:10.1016/j.aim.2004.12.004).

Record type: Article

Abstract

We define and study a numerical invariant of an algebraic group action which we call the canonical dimension. We then apply the resulting theory to the problem of computing the minimal number of parameters required to define a generic hypersurface of degree d in pn-1.

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More information

Published date: 1 December 2005
Keywords: algebraic group, g-variety, generic splitting field, essential dimension, canonical dimension, homogeneous forms

Identifiers

Local EPrints ID: 38409
URI: http://eprints.soton.ac.uk/id/eprint/38409
DOI: doi:10.1016/j.aim.2004.12.004
ISSN: 0001-8708
PURE UUID: 40ae26ec-05f2-407d-892d-341c1465456d

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Date deposited: 08 Jun 2006
Last modified: 15 Mar 2024 08:07

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Contributors

Author: Grégory Berhuy
Author: Zinovy Reichstein

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