矩阵矩阵的谱分解的相对奇异轨迹和Balmer谱
Relative singular locus and Balmer spectrum of matrix factorizations
摘要：
对于具有大量线丛的分离Noether格式$X$和$X$上的线丛$L$的非零因子$W\inΓ(X,L)$，我们对Landau-Ginzburg模型$(X,L,W)$的导出矩阵分解范畴${\rm DMF}(X,L,W)$的某些厚子范畴进行了分类.进一步，利用分类结果和Balmer张量三角几何理论，我们证明了张量三角范畴$({\rm DMF}(X,L,W), \otimes^{\frac{1}{2}})$的谱同胚于本文引入的$W$的零概型$X_0\subset X$的相对奇异轨迹${\rm Sing}(X_0/X)$.
英文摘要：
For a separated Noetherian scheme $X$ with an ample family of line bundles and a non-zero-divisor $W\inΓ(X,L)$ of a line bundle $L$ on $X$, we classify certain thick subcategories of the derived matrix factorization category ${\rm DMF}(X,L,W)$ of the Landau-Ginzburg model $(X,L,W)$. Furthermore, by using the classification result and the theory of Balmer's tensor triangular geometry, we show that the spectrum of the tensor triangulated category $({\rm DMF}(X,L,W), \otimes^{\frac{1}{2}})$ is homeomorphic to the relative singular locus ${\rm Sing}(X_0/X)$, introduced in this paper, of the zero scheme $X_0\subset X$ of $W$.
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