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We prove that Friedlander’s generalized isomorphism conjecture on the cohomology of algebraic groups, and hence the Isomorphism Conjecture for the cohomology of the complex algebraic Lie group G(ℂ) made discrete, are equivalent to the existence of an isoperimetric inequality in the...
We study how to minimize the number of invariants that is sufficient for the Whitney equisingularity of a one parameter deformation of corank one finitely determined holomorphic germ ƒ : (ℂ n , 0) → (ℂ n , 0). According to a result of Gaffney, these are the 0-stable invariants and all...
A resolution Z → X of a Poisson variety X is called Poisson if every Poisson structure on X lifts to a Poisson structure on Z . For symplectic varieties, we prove that Poisson resolutions coincide with symplectic resolutions. It is shown that for a smooth Poisson surface S , the natural...
Let be the open unit ball in ℂ d , d ≧ 1, and H d 2 be the space of analytic functions on determined by the reproducing kernel (1 − 〈 z , λ 〉) −1 . This reproducing kernel Hilbert space serves a universal role in the model theory for d -contractions, i.e. tuples T = ( T 1 ,…, T d )...
Let k be a field of characteristic zero, V a smooth, positive-dimensional, quasiprojective variety over k , and Q a nonempty divisor on V . Let K be the function field of V , and A ⊂ K the semilocal ring of Q . We prove the Diophantine undecidability of: (1) A , in all cases; (2) K , when k is...
A conjecture of Thurston asserts that a geometrically finite hyperbolic 3-manifold is completely determined by the bending data of its convex core. We prove this conjecture for small deformations of fuchsian manifolds.
Let Γ be a discrete finitely generated group. Let → T be a Γ-equivariant fibration, with fibers diffeomorphic to a fixed even dimensional manifold with boundary Z . We assume that Γ → → | Γ is a Galois covering of a compact manifold with boundary. Let ( D + (θ)) θ ∈ T be a...
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