论文标题
坡度的半可见性和正锥
Slope Semistability and Positive cones of Grassmann bundles
论文作者
论文摘要
让$ e $成为平滑复杂的投影型$ x $的等级$ r $的矢量捆绑包。在本文中，我们计算了Grassmann Bundle $ gr_x（k，e）中的除数的nef和pseudoeffeffection锥，$ k $ k $ - 二维子空间$ e $，其中$ 1 \ leq k \ leq leq等级（e）$，在$ x $ x $ x $ y上的假设上以及$ e $ e $ e $ e。特别是，我们表明nef锥和$ gr_x（k，e）$ cone的伪填充锥，并且仅当$ e $是$ x $的斜率半固定捆绑包，$ c_2（end（e））= 0 $。我们还讨论了$ gr_x（k，e）$上的通用商捆绑包$ q_k $的nef nef和empleness。
Let $E$ be a vector bundle of rank $r$ on a smooth complex projective variety $X$. In this article, we compute the nef and pseudoeffective cones of divisors in the Grassmann bundle $Gr_X(k,E)$ parametrizing $k$-dimensional subspaces of the fibers of $E$, where $1\leq k \leq rank(E)$, under assumptions on $X$ as well as on the vector bundle $E$. In particular, we show that nef cone and the pseudoeffective cone of $Gr_X(k,E)$ coincide if and only if $E$ is a slope semistable bundle on $X$ with $c_2(End(E))=0$. We also discuss about the nefness and ampleness of the universal quotient bundle $Q_k$ on $Gr_X(k,E)$.
