论文标题
关于Ulrich Vector Bundle的Chern类的积极性
On the positivity of the first Chern class of an Ulrich vector bundle
论文作者
论文摘要
我们研究了平滑的n维品种$ x \ subseteq \ mathbb p^n $在平滑的n维品种上的等级向量束E的阳性。我们证明，$ C_1（e）$对X中的线路不包含的每个子各种都非常积极。特别是如果X不覆盖线，则E很大，$ C_1（e）^n \ ge r^n $。此外，我们在表面上用$ c_1（e）^2 = 0 $和$ c_1（e）^2 = 0 $或$ c_1（e）（e）^3 = 0 $在三倍上（除了一些例外），用$ c_1（e）^2 = 0 $分类等级r ulrich vector捆绑包。
We study the positivity of the first Chern class of a rank r Ulrich vector bundle E on a smooth n-dimensional variety $X \subseteq \mathbb P^N$. We prove that $c_1(E)$ is very positive on every subvariety not contained in the union of lines in X. In particular if X is not covered by lines, then E is big and $c_1(E)^n \ge r^n$. Moreover we classify rank r Ulrich vector bundles E with $c_1(E)^2=0$ on surfaces and with $c_1(E)^2=0$ or $c_1(E)^3=0$ on threefolds (with some exceptions).
