# Base manifolds for fibrations of projective irreducible symplectic manifolds

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Let X be a holomorphic symplectic manifold, of dimension divisible by four, and Ïƒ be an antisymplectic involution of X. The fixed locus F of Ïƒ is a Lagrangian submanifold of X; we show that its Ã‚-genus is one. As an application, we determine all possibilities for the Chern numbers of F...

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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...

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

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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...

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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 SÃ©rÃ© and to Coti-Zelati, Ekeland, and SÃ©rÃ© [5]; [12], which were obtained by variational...

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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 Fintushelâ€“Stern knot surgery. These manifolds are usually not symplectically aspherical.

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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 Fomenkoâ€“Mischenko (translation of invariants) and Tarasov construct a polynomial subalgebra...