Computing invariants of algebraic group actions in arbitrary characteristic

Details Computing invariants of algebraic group actions in arbitrary characteristic Computing invariants of algebraic group actions in arbitrary characteristic

2007-04-19

arxiv.org/abs/0704.2594v1

Mathematics

Commutative Algebra

43 pages

Scientific paper

Let G be an affine algebraic group acting on an affine variety X. We present an algorithm for computing generators of the invariant ring K[X]^G in the case where G is reductive. Furthermore, we address the case where G is connected and unipotent, so the invariant ring need not be finitely generated. For this case, we develop an algorithm which computes K[X]^G in terms of a so-called colon-operation. From this, generators of K[X]^G can be obtained in finite time if it is finitely generated. Under the additional hypothesis that K[X] is factorial, we present an algorithm that finds a quasi-affine variety whose coordinate ring is K[X]^G. Along the way, we develop some techniques for dealing with non-finitely generated algebras. In particular, we introduce the finite generation locus ideal.

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