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arXiv · 1605.02795

Derived categories of noncommutative quadrics and Hilbert squares

Pieter Belmans·Theo Raedschelders
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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.

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Pieter Belmans, Theo Raedschelders. 2018-07-26. Derived categories of noncommutative quadrics and Hilbert squares. https://doi.org/10.1093/imrn%2Frny192

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