2005/05/04 by C. Roucairol, Roucairol, C.
Mathematics · #32C38 #32S40 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:32C38 #msc:32S40
paper · pdf · doi:10.48550/arxiv.math/0505075
arxiv created 2005/05/04 · arxiv updated 2009/12/01
In the D-modules theory, Gauss-Manin systems are defined by the direct image of the structure sheaf O by a morphism. A major theorem says that these systems have only regular singularities. This paper examines the irregularity of an analogue of the Gauss-Manin systems. It consists in the direct image complex of a D-module twisted by the exponential of a polynomial g by another polynomial f, where f and g are two polynomials in two variables. The analogue of the Gauss-Manin systems can have irregular singularities (at finite distance and at infinity). We express an invariant associated with the irregularity of these systems by the geometry of the map (f,g).