Mathematics – Algebraic Geometry
Scientific paper
2012-03-27
Mathematics
Algebraic Geometry
69 pages
Scientific paper
In this paper we consider holomorphic families of frescos (i.e. filtered differential equations with a regular singularity) and we construct a locally versal holomorphic family for every fixed Bernstein polynomial. We construct also several holomorphic parameters (a holomorphic parameter is a function defined on a set of isomorphism classes of frescos) which are quasi-invariant by changes of variable. This is motivated by the fact that a fresco is associated to a relative de Rham cohomology class on a one parameter degeneration of compact complex manifolds, up to a change of variable in the parameter. Then the value of a quasi-invariant holomorphic parameter on such data produces a holomorphic (quasi-)invariant of such a situation.
Barlet Daniel
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