论文标题
明确的Stillman界限
Explicit Stillman bounds for all degrees
论文作者
论文摘要
在2016年，Ananyan和Hochster证明了Stillman的猜想，通过显示出所有均匀理想的均匀上限的存在，在一个田间的多项式环中，最多由n形式的学位生成d。尚不清楚5度及更高学位形式的边界的显式值。本文的主要结果是针对所有学位的明确构建此类界限，其行为就像高度D^3/6+11d/6-4的电力塔。这是通过建立绑定的D（K，d）来完成的，该绑定的D（K，d）可以控制一个规则序列的理想序列的最小素数或较少形式的D度D形式的发电机数，并将其补充为Ananyan和Hochster的证明，以获得复发关系。
In 2016 Ananyan and Hochster proved Stillman's conjecture by showing the existence of a uniform upper bound for the projective dimension of all homogeneous ideals, in polynomial rings over a field, generated by n forms of degree at most d. Explicit values of the bounds for forms of degrees 5 and higher are not yet known. The main result of this article is the construction of explicit such bounds, for all degrees d, which behave like power towers of height d^3/6+11d/6-4. This is done by establishing a bound D(k,d), which controls the number of generators of a minimal prime over an ideal of a regular sequence of k or fewer forms of degree d, and supplementing it into Ananyan and Hochster's proof in order to obtain a recurrence relation.
