منابع مشابه
On Global Degree Bounds for Invariants
Let G be a linear algebraic group over a field K of characteristic 0. An integer m is called a global degree bound for G if for every linear representation V the invariant ring K[V ] is generated by invariants of degree at most m. We prove that if G has a global degree bound, then G must be finite. The converse is well known from Noether’s degree bound.
متن کاملDegree Bounds for Syzygies of Invariants
Suppose that G is a linearly reductive group. Good degree bounds for generators of invariant rings were given in [2]. Here we study the minimal free resolution of the invariant ring. Recently it was shown that if G is a finite linearly reductive group, then the ring of invariants is generated in degree ≤ |G| (see [5, 6, 3]). This extends the classical result of Noether who proved the bound in c...
متن کاملPolynomial degree bounds for matrix semi-invariants
We study the left-right action of SL n × SL n on m-tuples of n × n matrices with entries in an infinite field K. We show that invariants of degree n 2 − n define the null cone. Consequently, invariants of degree ≤ n 6 generate the ring of invariants if char(K) = 0. We also prove that for m ≫ 0, invariants of degree at least n⌊ √ n + 1⌋ are required to define the null cone. We generalize our res...
متن کاملSeparating invariants
This paper studies separating subsets of an invariant ring or, more generally, of any set consisting of functions. We prove that a subset of a finitely generated algebra always contains a finite separating subset. We also show that a general version of Noether’s degree bound holds for separating invariants, independently of the characteristic. The paper also contains a conceptual investigation ...
متن کاملPolarization of Separating Invariants
We prove a characteristic free version of Weyl’s theorem on polarization. Our result is an exact analogue of Weyl’s theorem, the difference being that our statement is about separating invariants rather than generating invariants. For the special case of finite group actions we introduce the concept of cheap polarization, and show that it is enough to take cheap polarizations of invariants of j...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2010
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2010.v17.n6.a15