Stillman's conjecture via generic initial ideals
Stillman's conjecture via generic initial ideals
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DOI：
10.1080/00927872.2019.1574806
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发表时间：
2019-01-01
影响因子：
0.7
通讯作者：
Leykin, Anton
中科院分区：
文献类型：
--
作者：
Draisma, Jan;Lason, Michal;Leykin, Anton
利用Erman-Sam-Snowden最近的工作，我们证明了无穷多个变量的有界度形式幂级数环中的非生成理想具有相对于分次逆字典序的非生成Grobner基。然后，我们结合联合收割机这一结果与第一作者的工作拓扑Noetherianity多项式函子给一个算法证明以下声明：理想在多项式环所产生的固定数量的齐次多项式的固定度只有有限数量的可能通用初始理想，独立的变量的数量，他们涉及和独立的特点地面领域。我们的算法输出不仅是一个有限的列表可能的通用初始理想，但也有限的描述相应的地层空间中的系数。
Using recent work by Erman-Sam-Snowden, we show that finitely generated ideals in the ring of bounded-degree formal power series in infinitely many variables have finitely generated Grobner bases relative to the graded reverse lexicographic order. We then combine this result with the first author's work on topological Noetherianity of polynomial functors to give an algorithmic proof of the following statement: ideals in polynomial rings generated by a fixed number of homogeneous polynomials of fixed degrees only have a finite number of possible generic initial ideals, independently of the number of variables that they involve and independently of the characteristic of the ground field. Our algorithm outputs not only a finite list of possible generic initial ideals, but also finite descriptions of the corresponding strata in the space of coefficients.