扭曲矩阵分解的Chern特征和高阶Herbrand差的消失
Chern Characters for Twisted Matrix Factorizations and the Vanishing of the Higher Herbrand Difference
摘要：
我们开发了一个理论的“ad”陈字符扭曲矩阵分解相关的计划$X$，线丛${\mathcal L}$，和一个定期的全球部分$W \in Γ(X, {\mathcal L})$。作为一个应用，我们建立了消失，在某些情况下，$h_c^R(M,N)$，更高的Herbrand差异，和$η_c^R(M,N)$，更高的余维类似物Hochster的θ配对，其中$R$是一个完整的交叉余维$c$孤立的奇点和$M$和$N$是双生成的$R$ -模块。具体地说，我们证明了这种消失，如果$R = Q/(f_1, \dots, f_c)$只有孤立奇点，$Q$是一个光滑的$k$ -代数，$k$是一个领域的特征$0$，$f_i$的形式一个正规序列，和$c \geq 2$。
英文摘要：
We develop a theory of ``ad hoc'' Chern characters for twisted matrix factorizations associated to a scheme $X$, a line bundle ${\mathcal L}$, and a regular global section $W \in Γ(X, {\mathcal L})$. As an application, we establish the vanishing, in certain cases, of $h_c^R(M,N)$, the higher Herbrand difference, and, $η_c^R(M,N)$, the higher codimensional analogue of Hochster's theta pairing, where $R$ is a complete intersection of codimension $c$ with isolated singularities and $M$ and $N$ are finitely generated $R$-modules. Specifically, we prove such vanishing if $R = Q/(f_1, \dots, f_c)$ has only isolated singularities, $Q$ is a smooth $k$-algebra, $k$ is a field of characteristic $0$, the $f_i$'s form a regular sequence, and $c \geq 2$.
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