Seshadri constants on some blow-ups of projective spaces

Abstract

Let $X_{r,s}^n$ denote the blow-up of ${\mathbb{P}}^n$ along $r$ general lines and $s$ general points. In this paper, we focus on $l$-very ample line bundles on $X_{0,s}^n$ and investigate their Seshadri constants with some restrictions on $s$. Additionally, we compute the nef cone of $X_{r,0}^3$ for $r\le 6$ and study the Seshadri constants of some ample line bundles on it. We also examine the Seshadri constants of some ample line bundles on $X_{r,0}^4$ ($r\le 7$) and $X_{r,0}^5$ ($r\le 5$).

17 pages, Published