论文标题
对维罗尼斯戒指的模棱两可的分辨率
Equivariant resolutions over Veronese rings
论文作者
论文摘要
在多项式环$ s = \ mathbf {k} [x_1，\ ldots，x_n] $中工作，其中$ \ mathbf {k} $是一个任意的交换戒指，带有$ 1 $，我们考虑$ d^{th} $ d^{th} $ veronese subalgebras subalgebras $ r = s^{（d） $ m = s^{（\ geq r，d）} $ $ s $。我们开发和使用与色带偏斜图相关的Schur函数的无特征理论作为构造简单$ gl_n（\ MathBf {k}）$ - Equivariant最小值$ r $ r $ r $ - 用于商环$ \ Mathbf {k} = r/r _+$的均值$ r $ - $ r $ r $ r $ r $ r $ r _+$和这些模块$ m $ m $ m $ m $。这些也导致了所有$ i $和$ i $和$ \ mathrm {hom} _r（m，m，m'）$的$ \ mathrm {tor}^r_i（m，m'）$的优雅描述。
Working in a polynomial ring $S=\mathbf{k}[x_1,\ldots,x_n]$ where $\mathbf{k}$ is an arbitrary commutative ring with $1$, we consider the $d^{th}$ Veronese subalgebras $R=S^{(d)}$, as well as natural $R$-submodules $M=S^{(\geq r, d)}$ inside $S$. We develop and use characteristic-free theory of Schur functors associated to ribbon skew diagrams as a tool to construct simple $GL_n(\mathbf{k})$-equivariant minimal free $R$-resolutions for the quotient ring $\mathbf{k}=R/R_+$ and for these modules $M$. These also lead to elegant descriptions of $\mathrm{Tor}^R_i(M,M')$ for all $i$ and $\mathrm{Hom}_R(M,M')$ for any pair of these modules $M,M'$.
