论文标题
家庭中半双相分解的模量空间
Moduli spaces of semiorthogonal decompositions in families
论文作者
论文摘要
对于平滑的投影型方案家族，我们证明，在该点的典型社区上，纤维独特变形的连贯滑轮的有界衍生的类别的半三相分解。我们使用对角捆的结构捆的分解和分解三角形之间的比较定理来做到这一点。然后，我们向后者应用一种变形理论，以固定靶标的形态学，这是在附录中开发的。 以此为关键成分，我们介绍了模量空间，该空间对光滑的投影家族的完美复合物类别进行了半三相分解。使用Artin的标准，我们表明这是家庭基础方案的典型代数空间，这可能是非Quasicopcact且不分开的。 我们将其推广到Orlov意义上的几何非共同方案家族。我们还仅定义了一个非平凡半双相分解的子函数分类，并猜想它是一个开放式和封闭的子空间。
For a smooth projective family of schemes we prove that a semiorthogonal decomposition of the bounded derived category of coherent sheaves of a fibre uniquely deforms over an étale neighbourhood of the point. We do this using a comparison theorem between semiorthogonal decompositions and decomposition triangles of the structure sheaf of the diagonal. We then apply to the latter a deformation theory for morphisms with a fixed lift of the target, which is developed in the appendix. Using this as a key ingredient we introduce a moduli space which classifies semiorthogonal decompositions of the category of perfect complexes of a smooth projective family. Using Artin's criterion, we show that this is an étale algebraic space over the base scheme of the family, which can be non-quasicompact and non-separated. We generalise this to families of geometric noncommutative schemes in the sense of Orlov. We also define a subfunctor classifying nontrivial semiorthogonal decompositions only, and conjecture it is an open and closed subspace.
