Combinatorial and Commutative Algebra Seminar 2:30 PM MSCS 514
Singularities of orthogonal and symplectic determinantal varieties Andras Lorincz, University of Oklahoma Host: Alessandra Costantini Note unusual date and time
Abstract: I will discuss the geometry of varieties of matrices defined by certain isotropic rank conditions, that are generalizations of the generic determinantal varieties. These show up naturally in the representation theory of symmetric quivers, and are closely related to some symmetric spaces as well as to some classical nullcones. I will describe the defining equations of such varieties, and determine those that are normal, and in characteristic 0 those that are Cohen-Macaulay and have rational singularities. I will explain the main ideas behind the proof that involve the fundamental theorems of invariant theory for the classical groups, Donkin’s theory of good filtrations, the generic perfection theorem, and Kempf’s collapsing of bundles.
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