Polynomial degree bounds for matrix semi-invariants
نویسندگان
چکیده
منابع مشابه
Polynomial 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...
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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...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2017
ISSN: 0001-8708
DOI: 10.1016/j.aim.2017.01.018