Singularities of Secant Varieties

被引：5

作者：

Chou, Chih-Chi ^{[1
]}

Song, Lei ^{[2
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

[2] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2018年 / 2018卷 / 09期

基金：

美国国家科学基金会;

关键词：

NORMALITY; SYZYGIES;

D O I：

10.1093/imrn/rnw321

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the singularities of the secant variety Sigma(X, L) associated to a smooth variety X embedded by a sufficiently positive adjoint line bundle L. We show that Sigma(X, L) is always Du Bois singular. Examples of secant varieties with worse singularities when L has weak positivity are provided. We also give a necessary and sufficient condition for Sigma(X, L) to have rational singularities.

引用

页码：2844 / 2865

页数：22

共 25 条

[1] Non-rational centers of log canonical singularities [J].

Alexeev, Valery ;

Hacon, Christopher D. .

JOURNAL OF ALGEBRA, 2012, 369 :1-15

[2]

Anderson D, 2014, P AM MATH SOC, V142, P409

[3]

[Anonymous], 2015, Math. Sci. Res. Inst. Publ.

[4]

Beauville A., 1996, COMPLEX ALGEBRAIC SU

[5]

BERTRAM A, 1992, J DIFFER GEOM, V35, P429

[6] SYZYGIES AND KOSZUL COHOMOLOGY OF SMOOTH PROJECTIVE VARIETIES OF ARBITRARY DIMENSION [J].

EIN, L ;

LAZARSFELD, R .

INVENTIONES MATHEMATICAE, 1993, 111 (01) :51-67

[7]

Fujino O, 2012, MICH MATH J, V61, P255

[8]

Fulton W, 1998, INTERSECTION THEORY, V2

[9] POTENTIALLY DU BOIS SPACES [J].

Graf, Patrick ;

Kovacs, Sandor J. .

JOURNAL OF SINGULARITIES, 2014, 8 :117-134

[10]

Hartshorne R., 1977, Algebraic geometry, Graduate Texts in Mathematics, pxvi

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