TITLE

Antisymplectic involutions of holomorphic symplectic manifolds

AUTHOR(S)
Beauville, Arnaud
PUB. DATE
April 2011
SOURCE
Journal of Topology;Apr2011, Vol. 4 Issue 2, p300
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Let X be a holomorphic symplectic manifold, of dimension divisible by four, and σ be an antisymplectic involution of X. The fixed locus F of σ is a Lagrangian submanifold of X; we show that its Â-genus is one. As an application, we determine all possibilities for the Chern numbers of F when X is a deformation of the Hilbert square of a K3 surface.
ACCESSION #
61150588

 

Related Articles

  • Base manifolds for fibrations of projective irreducible symplectic manifolds. Hwang, Jun-Muk // Inventiones Mathematicae;Dec2008, Vol. 174 Issue 3, p625 

    Given a projective irreducible symplectic manifold M of dimension 2 n, a projective manifold X and a surjective holomorphic map f: M? X with connected fibers of positive dimension, we prove that X is biholomorphic to the projective space of dimension n. The proof is obtained by exploiting two...

  • Connections on k-symplectic manifolds. Blaga, Adara M. // Balkan Journal of Geometry & Its Applications;2009, Vol. 14 Issue 2, p28 

    On a k-symplectic manifold will be defined a canonical connection which induces on the reduced manifold a canonical connection, too. Two reduced standard k-symplectic manifolds with respect to the action of a Lie group G are considered, and the relation between the induced canonical connections...

  • A NOTE ON THE WEHRHEIM-WOODWARD CATEGORY. WEINSTEIN, ALAN // Journal of Geometric Mechanics;Dec2011, Vol. 3 Issue 4, p507 

    Wehrheim and Woodward have shown how to embed all the canonical relations between symplectic manifolds into a category in which the composition is the usual one when transversality and embedding assumptions are satisfied. A morphism in their category is an equivalence class of composable...

  • Picard-Lefschetz theory and dilating â„‚*-actions. Seidel, Paul // Journal of Topology;Dec2015, Vol. 8 Issue 4, p1167 

    We consider â„‚*-actions on Fukaya categories of exact symplectic manifolds. Such actions can be constructed by dimensional induction, going from the fibre of a Lefschetz fibration to its total space. We explore applications to the topology of Lagrangian submanifolds, with an emphasis on...

  • Graph manifold ℤ-homology 3-spheres and taut foliations. Boileau, Michel; Boyer, Steven // Journal of Topology;2015, Vol. 8 Issue 2, p571 

    We show that a graph manifold which is a ℤ-homology 3-sphere not homeomorphic to either S³ or Σ(2, 3, 5) admits a horizontal foliation. This combines with known results to show that the conditions of not being an L-space, of having a left-orderable fundamental group and of admitting...

  • On the geometry of non-holonomic Lagrangian systems. de Leon, Manuel; de Diego, David M. // Journal of Mathematical Physics;Jul96, Vol. 37 Issue 7, p3389 

    Studies a geometric framework for non-holonomic Lagrangian system in terms of distribution on the configuration manifold. Product structure of the phase space of velocities; Obtainment of constrained dynamics by projecting the free dynamics; Constraint algorithm for a singular constrained system.

  • On a family of conformally flat minimal Lagrangian tori in â„‚ P 3. Mironov, A. // Mathematical Notes;Apr/May2007, Vol. 81 Issue 3/4, p329 

    We give a description of a family of minimal conformally flat Lagrangian tori in â„‚ P 3

  • Homoclinic Orbits and Lagrangian Embeddings. Lisi, Samuel T. // IMRN: International Mathematics Research Notices;Jan2008, Vol. 2008, p1 

    This paper introduces techniques of symplectic topology to the study of homoclinic orbits in Hamiltonian systems. The main result is a strong generalization of homoclinic existence results due to Séré and to Coti-Zelati, Ekeland, and Séré [5]; [12], which were obtained by variational...

  • Mechanics systems on para-K�hlerian manifolds of constant J-sectional curvature. Tekkoyun, Mehmet // Differential Geometry--Dynamical Systems;2010, p239 

    The goal of this paper is to present Euler-Lagrange and Hamiltonian equations on Rn2n which is a model of para-K�hlerian manifolds of constant J-sectional curvature. In conclusion, some differential geometrical and physical results on the related mechanic systems have been given.

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics