Derived categories of noncommutative quadrics and Hilbert squares

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.

21 pages. Small corrections + expanded proof of Lemma 2.1

References in corpus (1)

• Geometric realizations of quiver algebras

Cited by in corpus (3)

• Derived categories of (nested) Hilbert schemes
• Hilbert squares: derived categories and deformations
• Admissible subcategories in derived categories of moduli of vector bundles on curves