arXiv subjects

Tristan Torrelli

Publications and source records attributed to Tristan Torrelli.

4 recordsLinked to original sources

arXiv2008

Intersection homology D-Modules and Bernstein polynomials associated with a complete intersection

Let X be a complex analytic manifold. Given a closed subspace $Y\subset X$ of pure codimension p>0, we consider the sheaf of local algebraic cohomology $H^p_{[Y]}({\cal O}_X)$, and ${\cal L}(Y,X)\subset H^p_{[Y]}({\cal O}_X)$ the intersection homology D_X-Module of Brylinski-Kashiwara. We give here an algebraic characterization of the spaces Y such that L(Y,X) coincides with $H^p_{[Y]}({\cal O}_X)$, in terms of Bernstein-Sato functional equations.

math.AG↗

arXiv2007

Matrice magique associée à un germe de courbe plane et division par l'idéal Jacobien

In the ring of holomorphic functions at the origin of C^2, we consider the equation uf'_x+vf'_y=wf where f and w are given. We introduce intersection multiplicities relative to w and f'_y along the branches of f, and we study the solutions (u,v) using these valuations. As an application, we construct an explicit functional equation satisfied by f.

math.AG↗

arXiv2006

On meromorphic functions defined by a differential system of order 1, II

Given a nonzero germ h of holomorphic function on (C^n,0), we study the condition: ``the ideal Ann\_D 1/h is generated by operators of order 1''. When h defines a generic arrangement of hypersurfaces with an isolated singularity, we show that it is verified if and only if h is weighted homogeneous and -1 is the only integral root of its Bernstein-Sato polynomial. When h is a product, we give a process to test this last condition. Finally, we study some other related conditions.

math.AG↗

arXiv2005

Logarithmic comparison theorem and D-modules: an overview

Let D be a divisor in a complex analytic manifold X. A natural problem is to determine when the de Rham complex of meromorphic forms on X with poles along D is quasi-isomorphic to its subcomplex of logarithmic forms. In this mostly expository note, we recall the main results about this problem. In particular, we point out the relevance of the theory of D-modules to this topic.

math.AG↗