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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/9926

Title: A Semiregularity Map for Modules and Applications to Deformations
Authors: Buchweitz, Ragnar-Olaf
Flenner, Hubert
Keywords: Semiregularity Map
Modules and Applications
Issue Date: Jun-2003
Publisher: Kluwer Academic Publishers
Citation: Compositio math. vol.137, no.2(2003) Pgs. 135-210
Abstract: We construct a general semiregularity map for algebraic cycles as asked for by S.Bloch in 1972. The existence of such a semiregularity map has well known consequences for the structure of the Hilbert scheme and for the variational Hodge conjecture. Aside from generalizing and extending considerably previously known results in this direction, we give new applications to deformations of modules that encompass, for example, results of Artamkin and Mukai. The formation of the semiregularity map here involves powers of the cotangent complex, Atiyah classes, and trace maps, and is defined not only for subspaces of manifolds but for perfect complexes on arbitrary complex spaces. It generalizes in particular Illusie's treatment of the Chern character to the analytic context and specializes to Bloch's earlier description of the semiregularity map for locally complete intersections as well as to the infinitesimal Abel–Jacobi map for submanifolds.
URI: http://hdl.handle.net/1807/9926
ISSN: 0010-437X
Appears in Collections:Mathematics

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