On the deformation theory of pair (X, E)

Details On the deformation theory of pair (X, E) On the deformation theory of pair (X, E)

2008-09-02

arxiv.org/abs/0809.0344v1

Mathematics

Algebraic Geometry

8 pages. Comments are wellcome

Scientific paper

Huybrechts and Thomas recently constructed relative obstruction theory of objects of the derived category of coherent sheaves over smooth projective family. In this paper, we use this construction to obtain the absolute deformation-obstruction theory of the pair (X, E), with X smooth projective scheme and E perfect complex, and show that the obstruction theories for E, (X,E), and X fit into exact triangle as derived objects on the moduli space.

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