When is the self-intersection of a subvariety a fibration?

被引：24

作者：

Arinkin, Dima ^{[2
]}

Caldararu, Andrei ^{[1
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[2] Univ N Carolina, Dept Math, Chapel Hill, NC 27599 USA

来源：

ADVANCES IN MATHEMATICS | 2012年 / 231卷 / 02期

基金：

美国国家科学基金会;

关键词：

HKR isomorphism; Derived intersection theory; Derived algebraic geometry; HOCHSCHILD; DECOMPOSITION;

D O I：

10.1016/j.aim.2012.05.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We provide a necessary and sufficient condition for the derived self-intersection of a smooth subscheme inside a smooth scheme to be a fibration over the subscheme. As a consequence we deduce a generalized HKR isomorphism. We also investigate the relationship of our result to path spaces in homotopy theory, Buchweitz-Flenner formality in algebraic geometry, and draw parallels with similar results in Lie theory and symplectic geometry. (C) 2012 Published by Elsevier Inc.

引用

页码：815 / 842

页数：28

共 22 条

[1]

[Anonymous], 1971, GRUNDLEHREN MATH WIS

[2]

[Anonymous], 1964, Publications Mathematiques de l'IHES, P259, DOI 10.1007/BF02684747

[3] The global decomposition theorem for Hochschild (co-)homology of singular spaces via the Atiyah-Chern character [J].