Chern Classes of Splayed Intersections

被引：4

作者：

Aluffi, Paolo ^{[1
]}

Faber, Eleonore ^{[2
,3
]}

机构：

[1] Florida State Univ, Dept Math, Tallahassee, FL 32306 USA

[2] Univ Toronto Scarborough, Dept Comp & Math Sci, Toronto, ON M1A 1C4, Canada

[3] Inst Mittag Leffler, SE-18260 Djursholm, Sweden

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2015年 / 67卷 / 06期

基金：

奥地利科学基金会; 美国国家科学基金会;

关键词：

Splayed intersection; Chern-Schwartz-MacPherson class; Chern-Fulton class; splayed blowup; Segre class;

D O I：

10.4153/CJM-2015-010-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We generalize the Chern class relation for the transversal intersection of two nonsingular varieties to a relation for possibly singular varieties, under a splayedness assumption. We show that the relation for the Chern-Schwartz-MacPherson classes holds for two splayed hypersurfaces in a nonsingular variety, and under a strong splayedness assumption for more general subschemes. Moreover, the relation is shown to hold for the Chern-Fulton classes of any two splayed subschemes. The main tool is a formula for Segre classes of splayed subschemes. We also discuss the Chem class relation under the assumption that one of the varieties is a general very ample divisor.

引用

页码：1201 / 1218

页数：18

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