88 research outputs found
Deformations of algebraic schemes via Reedy–Palamodov cofibrant resolutions
No full textLet X be a Noetherian separated and finite dimensional scheme over a field K of characteristic zero. The goal of this paper is to study deformations of X over a differential graded local Artin K-algebra by using local Tate–Quillen resolutions, i.e., the algebraic analogous of the Palamodov's resolvent of a complex space. The above goal is achieved by describing the DG-Lie algebra controlling deformation theory of a diagram of differential graded commutative algebras, indexed by a direct Reedy category
Formal deformation theory in left-proper model categories
No full textWe develop the notion of deformation of a morphism in a left-proper model category. As an application we provide a geomet-ric/homotopic description of deformations of commutative (non-positively) graded differential algebras over a local DG-Artin ring
Formal deformation theory in left-proper model categories
No full textWe develop the notion of deformation of a morphism in a left-proper model category. As an application we provide a geomet-ric/homotopic description of deformations of commutative (non-positively) graded differential algebras over a local DG-Artin ring
Formality conjecture for minimal surfaces of Kodaira dimension 0
No full textLet be a polystable sheaf on a smooth minimal projective surface of Kodaira dimension 0. Then the differential graded (DG) Lie algebra of derived endomorphisms of is formal. The proof is based on the study of equivariant minimal models of DG Lie algebras equipped with a cyclic structure of degree 2 which is non-degenerate in cohomology, and does not rely (even for K3 surfaces) on previous results on the same subject
Formality conjecture for minimal surfaces of Kodaira dimension 0
No full textLet F be a polystable sheaf on a smooth minimal projective surface of Kodaira dimension 0. Then the differential graded (DG) Lie algebra RHom(F, F) of derived endomorphisms of F is formal. The proof is based on the study of equivariant L-infinity minimal models of DG Lie algebras equipped with a cyclic structure of degree 2 which is non-degenerate in cohomology, and does not rely (even for K3 surfaces) on previous results on the same subject
DEFORMATIONS OF POLYSTABLE SHEAVES ON SURFACES: QUADRATICITY IMPLIES FORMALITY
No full textWe study relations between the quadraticity of the Kuranishi family of a coherent sheaf on a complex projective scheme and the formality of the DG-Lie algebra of its derived endomorphisms. In particular, we prove that for a polystable coherent sheaf of a smooth complex projective surface the DG-Lie algebra of derived endomorphisms is forif i
Deformations of polystable sheaves on surfaces: quadraticity implies formality
No full textWe study relations between the quadraticity of the Kuranishi family of a coherent sheaf on a complex projective scheme and the formality of the DG-Lie algebra of its derived endomorphisms. In particular, we prove that for a polystable coherent sheaf of a smooth complex projective surface the DG-Lie algebra of derived endomorphisms is formal if and only if the Kuranishi family is quadratic
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