论文标题
Boij-Söderberg猜想的差分模块
Boij-Söderberg Conjectures for Differential Modules
论文作者
论文摘要
Boij-Söderberg理论给出了属于多项式环上属于有限长度模块的Betti表的组合描述$ s = k [x_1，\ ldots，x_n] $。我们认为，可以为分级差异$ s $模块的类似数值不变性提供类似的组合描述，这些数字不变性是链复合物的天然概括。我们证明了几个结果可以提供支持该猜想的证据，包括在$ \ Mathbb {p}^{n-1} $上的分级差异$ s $模型和相干滑轮之间的分类配对，以及在$ s = k [t] $的情况下证明了猜想的证明。
Boij-Söderberg theory gives a combinatorial description of the set of Betti tables belonging to finite length modules over the polynomial ring $S = k[x_1, \ldots, x_n]$. We posit that a similar combinatorial description can be given for analogous numerical invariants of graded differential $S$-modules, which are natural generalizations of chain complexes. We prove several results that lend evidence in support of this conjecture, including a categorical pairing between the derived categories of graded differential $S$-modules and coherent sheaves on $\mathbb{P}^{n-1}$ and a proof of the conjecture in the case where $S = k[t]$.
