English

Nef cones of nested Hilbert schemes of points on surfaces

Algebraic Geometry 2021-11-04 v2

Abstract

Let XX be the projective plane, a Hirzebruch surface, or a general K3K3 surface. In this paper, we study the birational geometry of various nested Hilbert schemes of points parameterizing pairs of zero-dimensional subschemes on XX. We calculate the nef cone for two types of nested Hilbert schemes: X[n+1,n]X^{[n+1,n]} and universal families. As an application, we recover a theorem of Butler on syzygies on Hirzebruch surfaces.

Keywords

Cite

@article{arxiv.1708.00903,
  title  = {Nef cones of nested Hilbert schemes of points on surfaces},
  author = {Tim Ryan and Ruijie Yang},
  journal= {arXiv preprint arXiv:1708.00903},
  year   = {2021}
}

Comments

23 Pages. IMRN, 2018