The MMP for deformations of Hilbert schemes of points on the projective plane

TL;DR

This paper explores the birational geometry of deformations of Hilbert schemes of points on the projective plane, establishing explicit links between stable base locus walls and Bridgeland stability walls, revealing differences from the classical Hilb P2.

Contribution

It provides an explicit correspondence between stable base locus walls and Bridgeland stability walls for deformed Hilbert schemes, extending previous work.

Findings

Deformed Hilb P2 has different birational geometry than Hilb P2.

Established explicit correspondence between different wall types.

Revealed new geometric properties of deformed Hilbert schemes.

Abstract

We study the birational geometry of deformations of Hilbert schemes of points on the projective plane P2. We complete the picture in the paper of Daniele Arcara, Aaron Bertram, Izzet Coskun and Jack Huizenga by giving an explicit correspondence between the stable base locus walls on the Neron-Severi space and the actual walls on the Bridgeland stability space. We show that the birational geometry of a deformed Hilb P2 is different from that of Hilb P2.