Marco Manetti

Publications (8)0 Total impact

• Source

  Available from: ArXiv

  Article: Semiregularity and obstructions of complete intersections

  Donatella Iacono, Marco Manetti
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  ABSTRACT: We prove that, on a smooth projective variety over an algebraically closed field of characteristic 0, the semiregularity map annihilates every obstruction to embedded deformations of a local complete intersection subvariety with extendable normal bundle. The proof is based on the theory of L-infinity algebras and Tamarkin-Tsigan calculus on the de Rham complex of DG-schemes.
  12/2011;
• Source

  Available from: ArXiv

  Article: Formality of Koszul brackets and deformations of holomorphic Poisson manifolds

  Domenico Fiorenza, Marco Manetti
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  ABSTRACT: We show that if a generator of a differential Gerstenhaber algebra satisfies certain Cartan-type identities, then the corresponding Lie bracket is formal. Geometric examples include the shifted de Rham complex of a Poisson manifold and the subcomplex of differential forms on a symplectic manifold vanishing on a Lagrangian submanifold, endowed with the Koszul bracket. As a corollary we generalize a recent result by Hitchin on deformations of holomorphic Poisson manifolds.
  09/2011;
• Source

  Available from: ArXiv

  Article: Posetted trees and Baker-Campbell-Hausdorff product

  Donatella Iacono, Marco Manetti
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  ABSTRACT: We introduce the combinatorial notion of posetted trees and we use it in order to write an explicit expression of the Baker-Campbell-Hausdorff formula.
  06/2011;
• Source

  Available from: ArXiv

  Article: An algebraic proof of Bogomolov-Tian-Todorov theorem

  Donatella Iacono, Marco Manetti
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  ABSTRACT: We give a completely algebraic proof of the Bogomolov-Tian-Todorov theorem. More precisely, we shall prove that if X is a smooth projective variety with trivial canonical bundle defined over an algebraically closed field of characteristic 0, then the L-infinity algebra governing infinitesimal deformations of X is quasi-isomorphic to an abelian differential graded Lie algebra. Comment: 20 pages, amsproc
  02/2009;
• Source

  Available from: ArXiv

  Article: A period map for generalized deformations

  Domenico Fiorenza, Marco Manetti
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  ABSTRACT: For every compact Kaehler manifold we give a canonical extension of Griffith's period map to generalized deformations, intended as solutions of Maurer-Cartan equation in the algebra of polyvector fields. Our construction involves the notion of Cartan homotopy and a canonical L-infinity structure on mapping cones of morphisms of differential graded Lie algebras.
  08/2008;
• Source

  Available from: ArXiv

  Article: Semicosimplicial DGLAs in deformation theory

  Domenico Fiorenza, Marco Manetti, Elena Martinengo
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  ABSTRACT: We identify Cech cocycles in nonabelian (formal) group cohomology with Maurer-Cartan elements in a suitable L-infinity algebra. Applications to deformation theory are described.
  04/2008;
• Source

  Available from: arxiv.org

  Article: L-infinity algebras, Cartan homotopies and period maps

  Domenico Fiorenza, Marco Manetti
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  ABSTRACT: We prove that, for every compact Kaehler manifold, the period map of its Kuranishi family is induced by a natural L-infinity morphism. This implies, by standard facts about L-infinity algebras, that the period map is a "morphism of deformation theories" and then commutes with all deformation theoretic constructions (e.g. obstructions).
  06/2006;
• Source

  Available from: ArXiv

  Article: L-infinity structures on mapping cones

  Domenico Fiorenza, Marco Manetti
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  ABSTRACT: We show that the mapping cone of a morphism of differential graded Lie algebras $\chi\colon L\to M$ can be canonically endowed with an $L_\infty$-algebra structure which at the same time lifts the Lie algebra structure on $L$ and the usual differential on the mapping cone. Moreover, this structure is unique up to isomorphisms of $L_\infty$-algebras. The associated deformation functor coincides with the one introduced by the second author in arXiv:math.AG/0507287.
  02/2006;