Wyniki wyszukiwania

1

Locally conformal symplectic nilmanifolds with no locally conformal Kähler metrics

100%

Bazzoni G., Marrero J. C.

Complex Manifolds

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2017

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tom 4

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nr 1

172-178

EN

We report on a question, posed by L. Ornea and M. Verbitsky in [32], about examples of compact locally conformal symplectic manifolds without locally conformal Kähler metrics. We construct such an example on a compact 4-dimensional nilmanifold, not the product of a compact 3-manifold and a circle.

2

The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry

76%

Seppi A.

Complex Manifolds

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2017

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tom 4

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nr 1

183-199

EN

Given a smooth spacelike surface ∑ of negative curvature in Anti-de Sitter space of dimension 3, invariant by a representation p: π1 (S) → PSL2ℝ x PSL2ℝ where S is a closed oriented surface of genus ≥ 2, a canonical construction associates to ∑ a diffeomorphism φ∑ of S. It turns out that φ∑ is a symplectomorphism for the area forms of the two hyperbolic metrics h and h' on S induced by the action of p on ℍ2 x ℍ2. Using an algebraic construction related to the flux homomorphism, we give a new proof of the fact that φ∑ is the composition of a Hamiltonian symplectomorphism of (S, h) and the unique minimal Lagrangian diffeomorphism from (S, h) to (S, h’).

3

Transverse Hilbert schemes and completely integrable systems

64%

Donin N. L. L.

Complex Manifolds

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2017

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tom 4

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nr 1

263-272

EN

In this paper we consider a special class of completely integrable systems that arise as transverse Hilbert schemes of d points of a complex symplectic surface S projecting onto ℂ via a surjective map p which is a submersion outside a discrete subset of S. We explicitly endow the transverse Hilbert scheme Sp[d] with a symplectic form and an endomorphism A of its tangent space with 2-dimensional eigenspaces and such that its characteristic polynomial is the square of its minimum polynomial and show it has the maximal number of commuting Hamiltonians.We then provide the inverse construction, starting from a 2ddimensional holomorphic integrable system W which has an endomorphism A: TW → TW satisfying the above properties and recover our initial surface S with W ≌ Sp[d].

Ograniczanie wyników

3 Complex Manifolds

1 Bazzoni G.

1 Donin N. L. L.

1 Marrero J. C.

1 Seppi A.

3 2017

Locally conformal symplectic nilmanifolds with no locally conformal Kähler metrics

The flux homomorphism on closed hyperbolic surfaces and Anti-de Sitter three-dimensional geometry

Transverse Hilbert schemes and completely integrable systems