Mathematics Colloquia and Seminars

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Let X be an algebraic variety equipped with the action of an algebraic group G. In this talk I will discuss some results on G-equivariant D-modules on X in the case when G acts on X with finitely many orbits. In this setting, the category of equivariant coherent D-modules is equivalent to the category of finite-dimensional representations of a quiver. We describe explicitly these categories in some special cases, when the quivers turn out to be of finite or tame representation type. We apply these results to local cohomology modules supported in orbit closures by describing their explicit D-module structure. In particular, we determine the Lyubeznik numbers of all determinantal rings, thus answering a question of M. Hochster.