Lower semi-continuity of the Waldschmidt constants

Abstract

In this paper, we study the Waldschmidt constant of a generalized fat point subscheme $Z=m_1{p}_1+\cdots +m_r{p}_r$ of ${\mathbb{P}}^2$, where $p_1,\cdots ,p_r$ are essentially distinct points on ${\mathbb{P}}^2$, satisfying the proximity inequalities. Furthermore, we prove its lower semi-continuity for $r\le 8$. Using this property, we also calculate the Waldschmidt constants of the fat point subschemes $Z=p_1+\cdots +p_5$ giving weak del Pezzo surfaces of degree 4.

25 pages, 29 figures

References in corpus (2)

• Resolutions of ideals of six fat points in P^2
• Configuration types and cubic surfaces