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Foliated structure of the Kuranishi space and isomorphisms of deformation families of compact complex manifolds

Laurent Meersseman (2011)

Annales scientifiques de l'École Normale Supérieure

Consider the following uniformization problem. Take two holomorphic (parametrized by some analytic set defined on a neighborhood of 0 in p , for some p > 0 ) or differentiable (parametrized by an open neighborhood of 0 in p , for some p > 0 ) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point t of the parameter space, the fiber over t of the first family is biholomorphic to the fiber over t of the second family. Then, under which conditions are the...

Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)

Antoine Douai, Claude Sabbah (2003)

Annales de l’institut Fourier

We associate to any convenient nondegenerate Laurent polynomial f on the complex torus ( * ) n a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of f (or its universal unfolding) and of the corresponding Hodge theory.

Generalized Hurwitz maps of the type S × V → W, anti-involutions, and quantum braided Clifford algebras

Julian Ławrynowicz, Jakub Rembieliński, Francesco Succi (1996)

Banach Center Publications

The notion of a J 3 -triple is studied in connection with a geometrical approach to the generalized Hurwitz problem for quadratic or bilinear forms. Some properties are obtained, generalizing those derived earlier by the present authors for the Hurwitz maps S × V → V. In particular, the dependence of each scalar product involved on the symmetry or antisymmetry is discussed as well as the configurations depending on various choices of the metric tensors of scalar products of the basis elements. Then...

Geometric and categorical nonabelian duality in complex geometry

Siegmund Kosarew (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The Leitmotiv of this work is to find suitable notions of dual varieties in a general sense. We develop the basic elements of a duality theory for varieties and complex spaces, by adopting a geometric and a categorical point of view. One main feature is to prove a biduality property for each notion which is achieved in most cases.

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