Simple cyclic covers of the plane and Seshadri constants of some general hypersurfaces in weighted projective space

Abstract

Let $X$ be a general hypersurface of degree $md$ in the weighted projective space with weights $1,1,1,m$ for some for $d\ge 2$ and $m\ge 3$. We prove that the Seshadri constant of the ample generator of the Néron-Severi space at a general point $x\in X$ lies in the interval $\left[\sqrt{d}-\frac{d}{m},\sqrt{d}\right]$ and thus approaches the possibly irrational number $\sqrt{d}$ as $m$ grows.

arXiv comment7 pages, comments are welcome