TITLE

Base manifolds for fibrations of projective irreducible symplectic manifolds

AUTHOR(S)
Hwang, Jun-Muk
PUB. DATE
December 2008
SOURCE
Inventiones Mathematicae;Dec2008, Vol. 174 Issue 3, p625
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
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 geometric structures at general points of X: the affine structure arising from the action variables of the Lagrangian fibration f and the structure defined by the variety of minimal rational tangents on the Fano manifold X.
ACCESSION #
35119679

 

Related Articles

  • Antisymplectic involutions of holomorphic symplectic manifolds. Beauville, Arnaud // Journal of Topology;Apr2011, Vol. 4 Issue 2, p300 

    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...

  • 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

  • Natural Star Products on Symplectic Manifolds and Quantum Moment Maps. Gutt, Simone; Rawnsley, John // Letters in Mathematical Physics;October/November2003, Vol. 66 Issue 1/2, p123 

    We define a natural class of star products: those which are given by a series of bidifferential operators which at order k in the deformation parameter have at most k derivatives in each argument. This class includes all the standard constructions of star products. We show that any such star...

  • Generalized Kähler Geometry, Gerbes, and all that. Zabzine, Maxim // Letters in Mathematical Physics;Oct2009, Vol. 90 Issue 1-3, p373 

    We review recent advances in generalized Kähler geometry while stressing the use of Poisson and symplectic geometry. The derivation of a generalized Kähler potential is sketched and relevant global issues are discussed.

  • Invariants of real symplectic 4-manifolds and lower bounds in real enumerative geometry. Welschinger, Jean-Yves // Inventiones Mathematicae;Oct2005, Vol. 162 Issue 1, p195 

    We first build the moduli spaces of real rational pseudo-holomorphic curves in a given real symplectic 4-manifold. Then, following the approach of Gromov and Witten [3, 19, 11], we define invariants under deformation of real symplectic 4-manifolds. These invariants provide lower bounds for the...

  • NON-KÄHLER SYMPLECTIC MANIFOLDS WITH TORIC SYMMETRIES. YI LIN; PELAYO, ALVARO // Quarterly Journal of Mathematics;Mar2011, Vol. 62 Issue 1, p103 

    Drawing on the classification of symplectic manifolds with coisotropic principal orbits by Duistermaat and Pelayo, in this note we exhibit families of compact symplectic manifolds, such that: (i) no two manifolds in a family are homotopically equivalent; (ii) each manifold in each family...

  • 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...

  • Lagrangian tori in closed 4-manifolds. Knapp, Adam C. // Journal of Topology;Apr2010, Vol. 3 Issue 2, p333 

    We use a result of Chekanov to obtain examples of smoothly but not symplectically isotopic Lagrangian tori in closed simply connected symplectic 4-manifolds arising from Fintushel–Stern knot surgery. These manifolds are usually not symplectically aspherical.

  • Fomenko—Mischenko Theory, Hessenberg Varieties, and Polarizations. Kostant, Bertram // Letters in Mathematical Physics;Oct2009, Vol. 90 Issue 1-3, p253 

    The symmetric algebra $${S(\mathfrak{g})}$$ over a Lie algebra $${\mathfrak{g}}$$ has the structure of a Poisson algebra. Assume $${\mathfrak{g}}$$ is complex semisimple. Then results of Fomenko–Mischenko (translation of invariants) and Tarasov construct a polynomial subalgebra...

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