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

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

2010-07-09

arxiv.org/abs/1007.1671v2

Mathematics

Algebraic Geometry

29pp., LaTeX

Scientific paper

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.

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