Covariants and the No-Name Lemma
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A close connection between the no-name lemma (concerning algebraic groups acting on vector bundles) and the existence of sufficiently many independent rational covariants is pointed out. In particular, this leads to a new natural proof of the no-name lemma. For linearly reductive groups, the approach has a refined variant based on integral covariants. This fits into the usual context of invariant theory, and yields a version of the no-name lemma that has a constructive nature.
The paper has been completely rewritten, more conclusive results are achieved
- Hungarian Academy of Science Hungary
- Hungarian Academy of Sciences Hungary
20G05, no-name lemma, Group actions on varieties or schemes (quotients), 14L30, 13A50, invariant theory, covariants, Mathematics - Algebraic Geometry, Rationality questions in algebraic geometry, FOS: Mathematics, Speiser's lemma, Representation Theory (math.RT), 13A50; 14L30; 20G05, Algebraic Geometry (math.AG), Mathematics - Representation Theory, Actions of groups on commutative rings; invariant theory
20G05, no-name lemma, Group actions on varieties or schemes (quotients), 14L30, 13A50, invariant theory, covariants, Mathematics - Algebraic Geometry, Rationality questions in algebraic geometry, FOS: Mathematics, Speiser's lemma, Representation Theory (math.RT), 13A50; 14L30; 20G05, Algebraic Geometry (math.AG), Mathematics - Representation Theory, Actions of groups on commutative rings; invariant theory
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