On Fujita's semi-ampleness in the rank one case

Fujita's very ampleness conjecture for singular toric varieties

We present a self-contained combinatorial approach to Fujita's conjectures in the toric case. Our main new result is a generalization of Fujita's very ampleness conjecture for toric varieties with arbitrary singularities. In an appendix, we use similar methods to give a new proof of an analogous toric generalization of Fujita's freeness conjecture due to Fujino.

Generation of jets and Fujita's jet ampleness conjecture on toric varieties

Jet ampleness of line bundles generalizes very ampleness by requiring the existence of enough global sections to separate not just points and tangent vectors, but also their higher order analogues called jets. We give sharp bounds guaranteeing that a line bundle on a projective toric variety is $k$-jet ample in terms of its intersection numbers with the invariant curves, in terms of the lattice lengths of the edges of its polytope, in terms of the higher concavity of its piecewise linear function and in terms of its Seshadri constant. For example, the tensor power $k+n-2$ of an ample line bund…

Fujita's Conjecture and Frobenius amplitude

We prove a version of Fujita's Conjecture in arbitrary characteristic, generalizing results of K.E. Smith. Our methods use the Frobenius morphism, but avoid tight closure theory. We also obtain versions of Fujita's Conjecture for coherent sheaves with certain ampleness properties.

移动塞沙迪常数与有效的 Fujita 型猜想

Moving Seshadri constants and effective Fujita-type conjectures

本文提出并探讨了新的 Fujita 猜想变体，涉及线性系统形式 |K_X + aK_X + bL| 的无基点性、非常量性和喷射放大性，并扩展了移动塞沙迪常数理论至任意域上的完备变种。

A characterization of Gorenstein toric Fano $n$-folds with index $n$ and Fujita's conjecture

We give a characterization of Gorenstein toric Fano varieties of dimension $n$ with index $n$ among toric varieties. As an application, we give a strong version of Fujita's freeness conjecture and also give a simple proof of Fujita's very ampleness conjecture on Gorenstein toric varieties.

关于一般超kähler流形的标准例子中Fujita猜想的探讨

On Fujita's conjecture for a general hyperkähler manifold in the standard series of examples

本文研究了极化为Hilb$^n$(K3)-型和Kum$^n$-型的模空间的基点自由性和非常充分性，并给出了这些空间连通和非空的条件。