On the geometry of the Hilbert schemes of points in the projective plane

Abstract

We classify minimal-degree curves in the Hilbert schemes of points on algebraic surfaces. When the algebraic surface is the projective plane, the nef cone and a flip structure of these Hilbert schemes are determined.

arXiv commentsubstantially revised, 19 pages

References in corpus (2)

• On the Cobordism Class of the Hilbert Scheme of a Surface
• The Chow groups and the motive of the Hilbert scheme of points on a surface

Cited by in corpus (2)

• Moduli of Bridgeland semistable objects on ${\mathbb{P}}^2$
• Some geometric properties of Hilbert schemes of space curves