An unobstructedness theorem is proved for deformations of compact holomorphic Poisson manifolds and applied to a class of examples. These include certain rational surfaces and Hilbert schemes of points on Poisson surfaces. We study in particular the Hilbert schemes of the projective plane and show that a generic deformation is determined by two parameters—an elliptic curve and a translation on ...

This paper analyses results from an investigation into the determinants of biotechnology innovation in New Zealand using a comprehensive new dataset. The theoretical framework is based on a synthesis of hypotheses drawn from four strands of the innovation literature and the empirical work utilises Poisson regression methods. The data provides strong support for the idea that smaller enterprises...

We prove a relative version of Kontsevich’s formality theorem. This theorem involves a manifold M and a submanifold C and reduces to Kontsevich’s theorem if C=M. It states that the DGLA of multivector fields on an infinitesimal neighbourhood of C is L∞-quasiisomorphic to the DGLA of multidifferential operators acting on sections of the exterior algebra of the conormal bundle. Applications to th...

background: iraq fought three wars in three consecutive decades, iran-iraq war (1980-1988), persian gulf war in 1991, and the iraq’s war in 2003. in the nineties of the last century and up to the present time, there have been anecdotal reports of increase in cancer in ninawa as in all provinces of iraq, possibly as a result of exposure to depleted uranium used by american troops in the last t...

We compute the space of Poisson traces on symmetric powers of affine symplectic varieties. In the case of symplectic vector spaces, we also consider the quotient by the diagonal translation action, which includes the quotient singularities T C/Sn associated to the type A Weyl group Sn and its reflection representation C . We also compute the full structure of the natural D-module, previously de...

The hypersurface in C3 with an isolated quasi-homogeneous elliptic singularity of type Ẽr, r = 6, 7, 8, has a natural Poisson structure. We show that the family of del Pezzo surfaces of the corresponding type Er provides a semiuniversal Poisson deformation of that Poisson structure. We also construct a deformation-quantization of the coordinate ring of such a del Pezzo surface. To this end, we ...