论文标题
稳定的Ulrich捆绑包在立方四倍上
Stable Ulrich bundles on cubic fourfolds
论文作者
论文摘要
在本文中，我们为在给定等级$ r $的立方四倍的$ x $上存在Ulrich捆绑包提供了必要和充分的条件。结果，我们表明，对于每个整数$ r \ ge 2 $，都有一个不可兼任等级的家族$ r $ r $ ulrich捆绑在某些立方四倍上，大致取决于$ r $参数，尤其是它们是野生表示类型的；立方四倍的特殊表面由Macaulay2明确构建；构建了一个新的$ 19 $维度的投影家族，构建了与某个立方四倍相关的十维不可还原式象征性歧管；对于某些立方四倍$ x $，存在算术上存在算术cohen-macaulay光滑的表面$ y \ subset x $，它不是交叉的$ x \ cap t $，用于编成codimension二次subvariety $ t \ subset \ subset \ bbb p^5 $。
In this paper, we give necessary and sufficient conditions for the existence of Ulrich bundles on cubic fourfold $X$ of given rank $r$. As consequences, we show that for every integer $r\ge 2$ there exists a family of indecomposable rank $r$ Ulrich bundles on the certain cubic fourfolds, depending roughly on $r$ parameters, and in particular they are of wild representation type; special surfaces on the cubic fourfolds are explicitly constructed by Macaulay2; a new $19$-dimensional family of projective ten-dimensional irreducible holomorphic symplectic manifolds associated to a certain cubic fourfold is constructed; and for certain cubic fourfold $X$, there exist arithmetically Cohen-Macaulay smooth surface $Y \subset X$ which are not an intersection $X \cap T$ for a codimension two subvariety $T \subset \Bbb P^5$.
