4,655 research outputs found
Deformations of holomorphic pseudo-symplectic Poisson manifolds
We prove unobstructed deformations for compact Kaehlerian even-dimensional
Poisson manifolds whose Poisson tensor degenerates along a divisor with mild
singularities. Examples include Hilbert schemes of del Pezzo surfaces.Comment: (the latest version strengthens the statement of the main theorem and
adds an example); to appear in Adv. Mat
Elliptic singularities on log symplectic manifolds and Feigin--Odesskii Poisson brackets
A log symplectic manifold is a complex manifold equipped with a complex
symplectic form that has simple poles on a hypersurface. The possible
singularities of such a hypersurface are heavily constrained. We introduce the
notion of an elliptic point of a log symplectic structure, which is a singular
point at which a natural transversality condition involving the modular vector
field is satisfied, and we prove a local normal form for such points that
involves the simple elliptic surface singularities
and . Our main application is to the classification of Poisson
brackets on Fano fourfolds. For example, we show that Feigin and Odesskii's
Poisson structures of type are the only log symplectic structures on
projective four-space whose singular points are all elliptic.Comment: 33 pages, comments welcom
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