论文标题
对称本地无用的决议和理性问题
Symmetric locally free resolutions and rationality problems
论文作者
论文摘要
我们表明，在$ \ mathbb {p}^2 $上的二足表面捆绑包的异性级别由其相关的凝糖绳束确定。作为一个应用程序，我们讨论了$ \ mathbb {p}^2 $的非常通用的四束束的稳定理性性，以及固定度的判别曲线。特别是，我们为某些判别数据构建了这些捆绑包的明确模型。除其他外，我们还获得了各种淋巴结孔穆凯（Mukai）四倍以及包含平面的立方四倍的杂种模型。最后，我们证明了几种类型的二次表面束的非理性性稳定。
We show that the birationality class of a quadric surface bundle over $\mathbb{P}^2$ is determined by its associated cokernel sheaves. As an application, we discuss stable-rationality of very general quadric bundles over $\mathbb{P}^2$ with discriminant curves of fixed degree. In particular, we construct explicit models of these bundles for some discriminant data. Among others, we obtain various birational models of a nodal Gushel-Mukai fourfold, as well as of a cubic fourfold containing a plane. Finally, we prove stable irrationality of several types of quadric surface bundles.
