论文标题
斯蒂尔曼的问题提交扭曲的通勤代数
Stillman's question for twisted commutative algebras
论文作者
论文摘要
令$ \ mathbf {a} _ {n，m} $为多项式环$ \ text {sym}（\ mathbf {c}^n \ otimes \ mathbf {c}^m）$，其自然动作$ \ \ m mathbf {gl} _m（gl} _m（gl} _m（\ m mathbf}）$。我们构建了一个$ \ mathbf {gl} _m（\ mathbf {c}）$的家庭 - 稳定的理想$ j_ {n，m} $ in $ \ mathbf {a} _ {a} _ {n，m} $，每个等同于一个同质的poldynomial as at as at ofivariant as at as at as at as at as at as polivariant at同等级别的poldynomial a g $ $ $ $ 2 $ 2 $ 2 $ 2 $ 2 $。使用Ananyan-Hochster原则，我们表明这个家庭的规律性是无限的。这是负面的问题，这是Erman-Sam-Snowden提出的关于Stillman猜想的概括的问题。
Let $\mathbf{A}_{n, m}$ be the polynomial ring $\text{Sym}(\mathbf{C}^n \otimes \mathbf{C}^m)$ with the natural action of $\mathbf{GL}_m(\mathbf{C})$. We construct a family of $\mathbf{GL}_m(\mathbf{C})$-stable ideals $J_{n, m}$ in $\mathbf{A}_{n, m}$, each equivariantly generated by one homogeneous polynomial of degree $2$. Using the Ananyan-Hochster principle, we show that the regularity of this family is unbounded. This negatively answers a question raised by Erman-Sam-Snowden on a generalization of Stillman's conjecture.
