The nef cones of and minimal-degree curves in the Hilbert schemes of points on certain surfaces

Zhenbo Qin and Yuping Tu

Vol. 284 (2016), No. 2, 439–453

DOI: 10.2140/pjm.2016.284.439

Abstract

We determine the nef cones of the Hilbert schemes of points on certain surfaces $X$ with $h^1\left(X,{\mathcal{O}}_X\right)$ = 0. Then we apply the results to Hirzebruch surfaces, and study the minimal-degree curves in the Hilbert schemes of points on Hirzebruch surfaces. Our results generalize those in Li, Qin, and Zhang (2003).

Keywords

nef cones, Hilbert schemes

Mathematical Subject Classification 2010

Primary: 14C05

Milestones

Received: 18 October 2015

Revised: 23 January 2016

Accepted: 20 February 2016

Published: 30 August 2016