An universal analytic structure is construted on the set of (singular) holomorphic foliations on a normal compact space. Such a foliation is by definition a coherent subsheaf of the holomorphic tangent sheaf stable by the Lie-bracket
We study compact Kähler manifolds admitting nonvanishing holomorphic vector fields, extending the classical birational classification of projective varieties with tangent vector fields to a classification modulo deformation in the Kähler case, and biholomorphic in the projective case. We introduce and analyze a new class of , and show that they form a smooth subspace in the Kuranishi space of deformations of the complex structure of . We extend Calabi’s theorem on the structure of compact Kähler...
The moduli space of stable vector bundles over a moving curve is constructed, and on this a generalized Weil-Petersson form is constructed. Using the local Riemann-Roch formula of Bismut-Gillet-Soulé it is shown that the generalized Weil-Petersson form is the curvature of the determinant line bundle, equipped with the Quillen metric, for a vector bundle on the fiber product of the universal moduli space with the universal curve.
Étant donnée une fonction régulière de moyenne nulle sur le tore de dimension , il est facile de voir que ses intégrales ergodiques au-dessus d’un flot de translation “générique”sont bornées. Il y a une dizaine d’années, A. Zorich a observé numériquement une croissance en puissance du temps de ces intégrales ergodiques au-dessus de flots d’hamiltoniens (non-exacts) “génériques”sur des surfaces de genre supérieur ou égal à , et Kontsevich et Zorich ont proposé une explication (conjecturelle) de...
Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the almost complex structure is integrable. We characterize twilled LR structures in terms of certain associated differential (bi)graded Lie and G(erstenhaber)-algebras; in particular the G-algebra arising from an almost complex structure is a (strict) d(ifferential) G-algebra...