Talk by P. Tortella

[Ugo Bruzzo]

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SISSA GEOMETRY & MATH PHYS SEMINARS
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Dr Pietro Tortella (Université d'Angers) will give a talk on

Logarithmic connections and the Atiyah algebroid of the normal bundle

on Friday, February 28th, at 2:30 pm in room 136, SISSA building A

Abstract:

Let X be a complex analytic manifold, and D a (simple normal crossing) divisor in it.
The Riemann-Hilbert correspondence establishes an equivalence between the category of local systems over X\D and the category of flat connections over X with logarithmic poles along D.

Logarithmic connections are representation of the Lie algebroid of vector fields on X tangent to the divisor D, and one can remark that the restriction of this bundle to the divisor admits a structure of Lie algebroid over D. It turns out that this is actually isomorphic to the normal bundle of D into X, and we will explain some interesting application of this simple remark. For example, we have a "local" correspondence between logarithmic connections and representations of the Atiyah Lie algebroid of the normal bundle, and some new insight to the problem of specialization of D-modules.