Chern character, infinitesimal Abel-Jacobi map and semi-regularity map

Using Chern character, we construct a natural transformation from the local Hilbert functor to a functor of Artin rings defined from Hochschild homology. This enables us to realize (after slight modification) the infinitesimal Abel-Jacobi map as a morphism between tangent spaces of two functors of A...

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Bibliographic Details
Published in:Communications in algebra Vol. 52; no. 8; pp. 3521 - 3541
Main Author: Yang, Sen
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.08.2024
Taylor & Francis Ltd
Subjects:
Chern character
Hochschild homology
Homology
Obstructions
Regularity
semi-regularity map
ISSN:0092-7872, 1532-4125
Online Access:Get full text
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Summary:Using Chern character, we construct a natural transformation from the local Hilbert functor to a functor of Artin rings defined from Hochschild homology. This enables us to realize (after slight modification) the infinitesimal Abel-Jacobi map as a morphism between tangent spaces of two functors of Artin rings and also enables us to reconstruct the semi-regularity map together with giving 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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content type line 14
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2024.2321514