论文标题
切线束的Seshadri常数
The Seshadri Constants of Tangent Sheaves on Toric Varieties
论文作者
论文摘要
在本文中，我们调查了完整的$ \ mathbb q $ -Factorial toverorial toric $ x $的Seshadri常数$ \ VAREPSILON（x，t_x; p）$。我们表明，$ \ varepsilon（x，t_x; 1）> 0 $，仅当以下语句成立为真：如果$ a_1v_1+\ cdots+cdots+a_kv_k = 0 $，其中$ a_i $是正真实数字，$ v_i $是pan $Δ$ ge $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x。基于结果，我们表明，带有$ \ varepsilon（x，t_x; p）的光滑的射弹品种$ x $对于x $中的某些$ p \对于投射空间是同构的，这是同构的，证实了M. Fulger和T. Murayama提出的猜想的特殊情况。
In this paper, we investigate the Seshadri constant $\varepsilon(X,T_X;p)$ of the tangent sheaf $T_X$ on a complete $\mathbb Q$-factorial toric variety $X$. We show that $\varepsilon(X,T_X;1)>0$ if and only if the following statement holds true: if $a_1v_1+\cdots +a_kv_k=0$ where $a_i$'s are positive real numbers and $v_i$'s are primitive generators of some rays in the fan $Δ$ that defines $X$, then $k\geq \dim X+1$. Based on the result, we show that a smooth projective toric variety $X$ with $\varepsilon(X,T_X;p)>0$ for some $p\in X$ is isomorphic to the projective space, confirming a special case of the conjecture proposed by M. Fulger and T. Murayama.
