Seshadri constants for vector bundles
Seshadri constants for vector bundles
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DOI：
10.1016/j.jpaa.2020.106559
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发表时间：
2019-03
影响因子：
0.8
通讯作者：
Mihai Fulger;T. Murayama
中科院分区：
文献类型：
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作者：
Mihai Fulger;T. Murayama
我们引入Seshadri常数的线丛在一个相对的设置。他们推广了经典的Seshadri常数的线丛上的射影簇和他们的推广到向量丛研究Beltrametti-Schneider-Sommese和Hacon。与经典理论有相似之处。特别是，我们给出了一个Seshadri型的充足率标准，我们与Seshadri常数射流分离和渐近基地。平滑度通常不是我们假设的一部分。因此，我们改进了一些已知的结果已经线丛。我们给出了我们的新版本的Seshadri常数的两个应用。首先，Mori的一个著名结果可以重述为：任何切丛在一点具有正Seshadri常数的Fano流形同构于射影空间。我们猜想Fano条件可以被去除。在这个方向的其他结果中，我们证明了曲面的猜想。其次，我们证明了我们的Seshadri常数可以用来控制分离的喷气机的直接图像的pluicanonical束，在一个相对的藤田型猜想的波帕和Schnell的精神。
We introduce Seshadri constants for line bundles in a relative setting. They generalize the classical Seshadri constants of line bundles on projective varieties and their extension to vector bundles studied by Beltrametti–Schneider–Sommese and Hacon. There are similarities to the classical theory. In particular, we give a Seshadri-type ampleness criterion, and we relate Seshadri constants to jet separation and to asymptotic base loci. Smoothness is generally not part of our assumptions. Thus we improve on some of the known results already for line bundles.We give two applications of our new version of Seshadri constants. First, a celebrated result of Mori can be restated as saying that any Fano manifold whose tangent bundle has positive Seshadri constant at a point is isomorphic to a projective space. We conjecture that the Fano condition can be removed. Among other results in this direction, we prove the conjecture for surfaces. Second, we prove that our Seshadri constants can be used to control separation of jets for direct images of pluricanonical bundles, in the spirit of a relative Fujita-type conjecture of Popa and Schnell.