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Derived categories of noncommutative quadrics and Hilbert squares (1605.02795v2)
Published 9 May 2016 in math.AG, math.QA, math.RA, and math.RT
Abstract: A noncommutative deformation of a quadric surface is usually described by a three-dimensional cubic Artin-Schelter regular algebra. In this paper we show that for such an algebra its bounded derived category embeds into the bounded derived category of a commutative deformation of the Hilbert scheme of two points on the quadric. This is the second example in support of a conjecture by Orlov. Based on this example, we formulate an infinitesimal version of the conjecture, and provide some evidence in the case of smooth projective surfaces.