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Lifting D -modules from positive to zero characteristic

João Pedro P. dos Santos (2011)

Bulletin de la Société Mathématique de France

We study liftings or deformations of D -modules ( D is the ring of differential operators from EGA IV) from positive characteristic to characteristic zero using ideas of Matzat and Berthelot’s theory of arithmetic D -modules. We pay special attention to the growth of the differential Galois group of the liftings. We also apply formal deformation theory (following Schlessinger and Mazur) to analyze the space of all liftings of a given D -module in positive characteristic. At the end we compare the problems...

On deformation method in invariant theory

Dmitri Panyushev (1997)

Annales de l'institut Fourier

In this paper we relate the deformation method in invariant theory to spherical subgroups. Let G be a reductive group, Z an affine G -variety and H ⊂ G a spherical subgroup. We show that whenever G / H is affine and its semigroup of weights is saturated, the algebra of H -invariant regular functions on Z has a G -invariant filtration such that the associated graded algebra is the algebra of regular functions of some explicit horospherical subgroup of G . The deformation method in its usual form, as developed...

The Hilbert scheme of space curves of small diameter

Jan Oddvar Kleppe (2006)

Annales de l’institut Fourier

This paper studies space curves C of degree d and arithmetic genus g , with homogeneous ideal I and Rao module M = H * 1 ( I ˜ ) , whose main results deal with curves which satisfy 0 Ext R 2 ( M , M ) = 0 (e.g. of diameter, diam M ≤ 2 ). For such curves we find necessary and sufficient conditions for unobstructedness, and we compute the dimension of the Hilbert scheme, H ( d , g ) , at ( C ) under the sufficient conditions. In the diameter one case, the necessary and sufficient conditions coincide, and the unobstructedness of C turns out to be equivalent to the...

Unobstructedness and dimension of families of Gorenstein algebras.

Jan O. Kleppe (2007)

Collectanea Mathematica

The goal of this paper is to develop tools to study maximal families of Gorenstein quotients A of a polynomial ring R. We prove a very general theorem on deformations of the homogeneous coordinate ring of a scheme Proj(A) which is defined as the degeneracy locus of a regular section of the dual of some sheaf M of rank r supported on say an arithmetically Cohen-Macaulay subscheme Proj(B) of Proj(R). Under certain conditions (notably; M maximally Cohen-Macaulay and ∧r M ≈ KB(t) a twist of the canonical...

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