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Daisuke Matsushita 《Mathematische Annalen》2001,321(4):755-773
We classify singular fibres over general points of the discriminant locus of projective Lagrangian fibrations over 4-dimensional
holomorphic symplectic manifolds. The singular fibre F is the following either one: F is isomorphic to the product of an elliptic curve and a Kodaira singular fibre up to finite unramified covering or F is a normal crossing variety consisting of several copies of a minimal elliptic ruled surface of which the dual graph is
Dynkin diagram of type or . Moreover, we show all types of the above singular fibres actually occur.
Received: 10 March 2000 / Revised version: 29 September 2000 / Published online: 24 September 2001 相似文献
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We prove in this paper that if G is a domain in the complex plane satisfying appropriate topological or geometrical conditions, then there exists a large (dense or closed infinite-dimensional) linear submanifold of boundary-regular holomorphic functions on G all of whose nonzero members are not continuable across any boundary point of G. 相似文献
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Bernard Shiffman Steve Zelditch 《Proceedings of the American Mathematical Society》2003,131(1):291-302
We define a Gaussian measure on the space of almost holomorphic sections of powers of an ample line bundle over a symplectic manifold , and calculate the joint probability densities of sections taking prescribed values and covariant derivatives at a finite number of points. We prove that they have a universal scaling limit as . This result will be used in another paper to extend our previous work on universality of scaling limits of correlations between zeros to the almost-holomorphic setting.
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Let M be an open manifold with a symplectic form Ω, and N a manifold with dimN<dimM. We prove that submersions with symplectic fibres satisfy the h-principle. Such submersions define Dirac manifold structures on the given manifold. As an application to this result we show that CPn?CPk−1 admits a submersion into R2(2k−n) with symplectic fibres for n/2<k?n. 相似文献
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Misha Verbitsky 《Selecta Mathematica, New Series》2005,10(4):551-559
For any subvariety of a compact holomorphic symplectic K?hler manifold, we define the symplectic Wirtinger number W(X). We show that
W(X) \leqslant 1,W(X) \leqslant 1, and the equality is reached if and only if the subvariety
X ì MX \subset M is trianalytic, i.e. compatible with the hyperk?hler structure on M. For a sequence
X1 ? X2 ? ?Xn ? MX_1 \to X_2 \to \ldots X_n \to M of immersions of simple holomorphic symplectic manifolds, we show that
W( X1 ) \leqslant W( X2 ) \leqslant ?\leqslant W( Xn ).W\left( {X_1 } \right) \leqslant W\left( {X_2 } \right) \leqslant \ldots \leqslant W\left( {X_n } \right). 相似文献
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As an extension of local geodesic symmetries we study here local reflections with respect to a topologically embedded submanifoldP in a Riemannian manifold (M, g). First we derive a criterion for isometric reflections. Then we study holomorphic and symplectic reflections on an almost Hermitian manifold. In particular we focus on the influence of these reflections on the intrinsic and extrinsic geometry of the submanifold. Finally we treat these three kinds of reflections and their relationship when the ambient manifold is a locally Hermitian symmetric space. The results are derived by the use of Jacobi vector fields. 相似文献
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Misha Verbitsky 《Selecta Mathematica, New Series》2004,10(4):551-559
For any subvariety of a compact holomorphic symplectic Kähler manifold, we define the symplectic Wirtinger number W(X). We show that
and the equality is reached if and only if the subvariety
is trianalytic, i.e. compatible with the hyperkähler structure on M. For a sequence
of immersions of simple holomorphic symplectic manifolds, we show that
相似文献
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Ion Alexandru Mihai 《Transformation Groups》2007,12(3):573-599
We define the odd symplectic Grassmannians and flag manifolds, which are smooth projective varieties equipped with an action
of the odd symplectic group, analogous to the usual symplectic Grassmannians and flag manifolds. Contrary to the latter, which
are the flag manifolds of the symplectic group, the varieties we introduce are not homogeneous. We argue nevertheless that
in many respects the odd symplectic Grassmannians and flag manifolds behave like homogeneous varieties; in support of this
claim, we compute the automorphism group of the odd symplectic Grassmannians and we prove a Borel-Weil-type theorem for the
odd symplectic group. 相似文献
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Alan Weinstein 《Advances in Mathematics》1980,37(3):239-250
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We study holomorphic flows on Stein manifolds. We prove that a holomorphic flow with isolated singularities and a dicritical
singularity of the form
on a Stein manifold
with
, is globally analytically linearizable; in particular M is biholomorphic to
. A complete stability result for periodic orbits is also obtained.
Bruno Scárdua: Partially supported by ICTP-Trieste-Italy.
Received: 27 September 2006 相似文献
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We study the asymptotic of the generalized Bergman kernels of the renormalized Bochner–Laplacian on high tensor powers of a positive line bundle on compact symplectic manifolds. To cite this article: X. Ma, G. Marinescu, C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
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M. Ferná ndez V. Muñ oz L. Ugarte 《Transactions of the American Mathematical Society》2007,359(4):1851-1873
For a symplectic manifold, the harmonic cohomology of symplectic divisors (introduced by Donaldson, 1996) and of the more general symplectic zero loci (introduced by Auroux, 1997) are compared with that of its ambient space. We also study symplectic manifolds satisfying a weakly Lefschetz property, that is, the -Lefschetz property. In particular, we consider the symplectic blow-ups of the complex projective space along weakly Lefschetz symplectic submanifolds . As an application we construct, for each even integer , compact symplectic manifolds which are -Lefschetz but not -Lefschetz.
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We construct examples of symplectic half-flat manifolds on compact quotients of solvable Lie groups. We prove that the Calabi-Yau
structures are not rigid in the class of symplectic half-flat structures. Moreover, we provide an example of a compact 6-dimensional
symplectic half-flat manifold whose real part of the complex volume form is d-exact. Finally we discuss the 4-dimensional case.
This work was supported by the Projects M.I.U.R. “Geometric Properties of Real and Complex Manifolds”, “Riemannian Metrics
and Differentiable Manifolds” and by G.N.S.A.G.A. of I.N.d.A.M. 相似文献
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We study the dynamics of Hamiltonian diffeomorphisms on convex symplectic manifolds. To this end we first establish an explicit
isomorphism between the Floer homology and the Morse homology of such a manifold, and then use this isomorphism to construct
a biinvariant metric on the group of compactly supported Hamiltonian diffeomorphisms analogous to the metrics constructed
by Viterbo, Schwarz and Oh. These tools are then applied to prove and reprove results in Hamiltonian dynamics. Our applications
comprise a uniform lower estimate for the slow entropy of a compactly supported Hamiltonian diffeomorphism, the existence
of infinitely many non-trivial periodic points of a compactly supported Hamiltonian diffeomorphism of a subcritical Stein
manifold, new cases of the Weinstein conjecture, and, most noteworthy, new existence results for closed trajectories of a
charge in a magnetic field on almost all small energy levels. We shall also obtain some new Lagrangian intersection results.
Partially supported by the Swiss National Foundation.
Supported by the Swiss National Foundation and the von Roll Research Foundation. 相似文献