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arXiv · 2109.10626

Chern character, semi-regularity map and obstructions

Sen Yang
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Abstract

Using Chern character, we construct a natural transformation from the local Hilbert functor to a functor of Artin rings defined from Hochschild homology, which allows us to reconstruct the semi-regularity map and the infinitesimal Abel-Jacobi map. Combining that construction of the semi-regularity map with obstruction theory of functors of Artin rings, we give a different proof of a theorem of Bloch stating that the semi-regularity map annihilates certain obstructions to embedded deformations of a closed subvariety which is a locally complete intersection.

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Sen Yang. 2021-09-22. Chern character, semi-regularity map and obstructions. https://arxiv.org/abs/2109.10626

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