SMALL SUBALGEBRAS OF POLYNOMIAL RINGS AND STILLMAN'S CONJECTURE
SMALL SUBALGEBRAS OF POLYNOMIAL RINGS AND STILLMAN'S CONJECTURE
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DOI：
10.1090/jams/932
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发表时间：
2020-01-01
影响因子：
3.9
通讯作者：
Hochster, Melvin
中科院分区：
文献类型：
--
作者：
Ananyan, Tigran;Hochster, Melvin
取正整数。我们证明了在具有任意特征的代数闭域上的多项式环不变量中，由大多数形式的次生成的任何-子代数最多包含在由形式的次生成的a-子代数中，其中不依赖于，使得这些形式是正则序列，并且对于由在张成空间中的形式生成的任何理想，环满足Serre条件。这些结果暗示了M. Stillman的一个猜想，即一个产生子是度的形式的产生子理想的射影维是有界独立的。我们还证明了存在这样一个初等分解，使得该分解的所有数值不变量（例如，所有出现的素数和初等理想的初等分量的个数和产生器的次数）都是有界独立的。参考文献
Letbe positive integers. We show that in a polynomial ringinvariables over an algebraically closed fieldof arbitrary characteristic, any-subalgebra ofgenerated overby at mostforms of degree at mostis contained in a-subalgebra ofgenerated byformsof degree, wheredoes not depend onor, such that these forms are a regular sequence and such that for any idealgenerated by forms that are in the-span of, the ringsatisfies the Serre condition. These results imply a conjecture of M. Stillman asserting that the projective dimension of an-generator idealofwhose generators are forms of degreeis bounded independent of. We also show that there is a primary decomposition ofsuch that all numerical invariants of the decomposition (eg, the number of primary components and the degrees and numbers of generators of all of the prime and primary ideals occurring) are bounded independent of. References