We study infinitesimal 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, for example, 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 | − mKX|, for some positive integer m.
Deformations and Obstructions of Pairs (X, D)
IACONO, Donatella
2015-01-01
Abstract
We study infinitesimal 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, for example, 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 | − mKX|, for some positive integer m.File in questo prodotto:
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