论文标题
二次表面束的残余类别
Residual categories of quadric surface bundles
论文作者
论文摘要
我们表明，二次表面束的残差类别等于以下假设下的某些方案的（扭曲）衍生类别。情况1：二次表面束具有平滑的截面。情况2：二次表面束的总空间光滑，底座是光滑的表面。在情况1中，我们提供了两个证据，将方案描述为双曲线还原和分别是线条相对希尔伯特方案的子处理。在情况2中，通过对线的相对希尔伯特方案进行双重转化来获得扭曲的方案。最后，我们将结果应用于某些四边形的完整交集。
We show that the residual categories of quadric surface bundles are equivalent to the (twisted) derived categories of some scheme under the following hypotheses. Case 1: The quadric surface bundle has a smooth section. Case 2: The total space of the quadric surface bundle is smooth and the base is a smooth surface. We provide two proofs in Case 1 describing the scheme as the hyperbolic reduction and as a subscheme of the relative Hilbert scheme of lines, respectively. In Case 2, the twisted scheme is obtained by performing birational transformations to the relative Hilbert scheme of lines. Finally, we apply the results to certain complete intersections of quadrics.
