论文标题
Del Pezzo表面的可允许子类别
Admissible subcategories of del Pezzo surfaces
论文作者
论文摘要
我们研究了在del pezzo表面和理性椭圆表面上相干滑轮的派生类别的可允许的子类别。使用可接受的子类别和反典型的除数之间的关系，我们证明了以下结果。首先，我们通过表明每个人都通过一个完整的特殊集合的子集合而生成的所有可接受的子类别，从而对投射平面进行了分类。其次，我们表明Del Pezzo表面的派生类别不包含任何幻影子类别。这提供了大于具有一些非平凡的可允许子类别的尺寸的品种的第一个示例，但事实证明不包含幻影。我们还证明，在表面上平滑（-1） - 弯曲中以理论上支持的任何可接受的子类别都是由该曲线的结构捆的某种扭曲而产生的。
We study admissible subcategories of derived categories of coherent sheaves on del Pezzo surfaces and rational elliptic surfaces. Using a relation between admissible subcategories and anticanonical divisors we prove the following results. First, we classify all admissible subcategories of the projective plane by showing that each is generated by a subcollection of a full exceptional collection. Second, we show that the derived categories of del Pezzo surfaces do not contain any phantom subcategories. This provides first examples of varieties of dimension larger than one that have some nontrivial admissible subcategories, but provably do not contain phantoms. We also prove that any admissible subcategory supported set-theoretically on a smooth (-1)-curve in a surface is generated by some twist of the structure sheaf of that curve.
