论文标题
家庭中衍生类别的不可分解性
Indecomposability of derived categories in families
论文作者
论文摘要
我们在平滑的投影家族中使用半双相分解的模量空间，第二个作者是第二个和第四位作者，我们提出了一种新颖的方法来针对派生类别的类别进行难以解决性问题。 Modulo对模量空间的结构进行了自然的猜想，我们既给出一般的结果，又通过将其与家庭规范基础基因座的行为联系起来，讨论了家庭中不可塑性的行为的有趣明确例子。这些示例是曲线的对称能力，具有较大典型基座基因座的某些常规表面以及表面上的点点方案。曲线对称能力的不可分解性已通过其他方式解决，其他情况仍然开放，我们希望我们对基地基因座的分析将证明有助于找到无条件的证明。
Using the moduli space of semiorthogonal decompositions in a smooth projective family, introduced by the second, the third and the fourth author, we propose a novel approach to indecomposability questions for derived categories. Modulo a natural conjecture on the structure of the moduli space, we give both general results, and discuss interesting explicit examples of the behaviour of indecomposability in families, by relating it to the behaviour of the canonical base locus in families. These examples are symmetric powers of curves, certain regular surfaces of general type with large canonical base locus, and Hilbert schemes of points on surfaces. Indecomposability for symmetric powers of curves has been settled via other means, the other cases remain open and we expect that our analysis of the base locus will prove instrumental in finding unconditional proofs.
