Chern character, semi-regularity map and obstructions

2021/09/22 by Yang, Sen
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2109.10626

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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