In this paper we develop a graded tilting theory for gauged Landau–Ginzburg models of regular sections in vector bundles over projective varieties. Our main theoretical result describes—under certain conditions—the bounded derived category of the zero locus $Z(s)$ of such a section s as a graded singularity category of a non-commutative quotient algebra $\Lambda / {\langle s \rangle} : D^b (\operatorname{coh}Z(s)) \simeq D^\mathrm{gr}_\mathrm{sg} \Lambda / {\langle s \rangle}$. Our geometric applications all come from homogeneous gauged linear sigma models. In this case Λ is a graded noncommutative resolution of the invariant ring which defines the $\mathbb{C}^\ast$-equivariant affine GIT quotient of the model. We obtain algebraic descriptions of the derived categories of the following families of varieties: 1. Complete intersections. 2. Isotropic symplectic and orthogonal Grassmannians. 3. Beauville–Donagi IHS 4-folds.

中文翻译：

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用于倾斜的Landau–Ginzburg模型和几何应用的渐变倾斜

在本文中，我们针对投影品种上矢量束中正则截面的规范Landau–Ginzburg模型的测距倾斜理论进行了开发。我们的主要理论结果在某些条件下将此类截面s的零轨迹$ Z（s）$的有界派生类别描述为非交换商代数$ \ Lambda / {\ langle s \ rangle}：D ^ b（\ operatorname {coh} Z（s））\ simeq D ^ \ mathrm {gr} _ \ mathrm {sg} \ Lambda / {\ langle s \ rangle} $。我们的几何应用全部来自均质的线性sigma模型。在这种情况下，Λ是不变环的分级非交换分辨率，它定义了模型的\\ mathbb {C} ^ \ ast $-等价仿射GIT商。我们获得以下变种家族的派生类别的代数描述：1.完整交集。2。各向同性辛和正交Grassmannian。3. Beauville–Donagi IHS 4倍。