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arXiv · 1302.1149

Deformations and obstructions of pairs (X,D)

Donatella Iacono
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Abstract

We study deformations of pairs (X,D), with X smooth projective variety and D a smooth or a normal crossing divisor, defined over an algebraically closed field of characteristic 0. Using the differential graded Lie algebras theory and the Cartan homotopy construction, we are able to prove in a completely algebraic way the unobstructedness of the deformations of the pair (X,D) in many cases, e.g., whenever (X,D) is a log Calabi-Yau pair, in the case of a smooth divisor D in a Calabi Yau variety X and when D is a smooth divisor in |-m K_X|, for some positive integer m.

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Donatella Iacono. 2013-02-05. Deformations and obstructions of pairs (X,D). https://doi.org/10.1093/imrn%2Frnu242

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