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2019•arXiv (Cornell University)Open access

Homotopy abelianity of the DG-Lie algebra controlling deformations of pairs (variety with trivial canonical bundle, line bundle)

Donatella Iacono, Marco Manetti

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Abstract

We investigate the deformations of pairs (X,L), where L is a line bundle on a smooth projective variety X, defined over an algebraically closed field of characteristic 0. In particular, we prove that the DG-Lie algebra controlling the deformations of the pair (X,L) is homotopy abelian whenever X has trivial canonical bundle, and so these deformations are unobstructed.

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What this paper is about

We investigate the deformations of pairs (X,L), where L is a line bundle on a smooth projective variety X, defined over an algebraically closed field of characteristic 0. In particular, we prove that the DG-Lie algebra controlling the deformations of the pair (X,L) is homotopy abelian whenever X has trivial canonical bundle, and so these deformations are unobstructed.

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Available abstract

We investigate the deformations of pairs (X,L), where L is a line bundle on a smooth projective variety X, defined over an algebraically closed field of characteristic 0. In particular, we prove that the DG-Lie algebra controlling the deformations of the pair (X,L) is homotopy abelian whenever X has trivial canonical bundle, and so these deformations are unobstructed.

Key concepts: Mathematics, Line bundle, Lie algebra, Pure mathematics, Projective variety, Canonical bundle, Bundle, Graded Lie algebra

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