Nef cones of Hilbert schemes of points on surfaces

被引：15

作者：

Bolognese, Barbara ^{[1
]}

Huizenga, Jack ^{[2
]}

Lin, Yinbang ^{[1
]}

Riedl, Eric ^{[3
]}

Schmidt, Benjamin ^{[4
]}

Woolf, Matthew ^{[3
]}

Zhao, Xiaolei ^{[1
]}

机构：

[1] Northeastern Univ, Dept Math, Boston, MA 02115 USA

[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[3] Univ Illinois, Dept Math Stat & CS, Chicago, IL 60607 USA

[4] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

来源：

ALGEBRA & NUMBER THEORY | 2016年 / 10卷 / 04期

基金：

美国国家科学基金会;

关键词：

Hilbert schemes; surfaces; nef cone; ample cone; birational geometry; Bridgeland stability; STABILITY CONDITIONS; ALGEBRAIC SURFACE; BRIDGELAND STABILITY; BIRATIONAL GEOMETRY; MODULI SPACES; EMBEDDINGS; FAMILIES; BUNDLES; PLANE;

D O I：

10.2140/ant.2016.10.907

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a smooth projective surface of irregularity 0. The Hilbert scheme X-[n] of n points on X parametrizes zero-dimensional subschemes of X of length n. We discuss general methods for studying the cone of ample divisors on X-[n]. We then use these techniques to compute the cone of ample divisors on X-[n] for several surfaces where the cone was previously unknown. Our examples include families of surfaces of general type and del Pezzo surfaces of degree 1. The methods rely on Bridgeland stability and the positivity lemma of Bayer and Macri.

引用

页码：907 / 930

页数：24

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