Derived Categories of Noncommutative Quadrics and Hilbert Squares
Derived Categories of Noncommutative Quadrics and Hilbert Squares
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DOI：
10.1093/imrn/rny192
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发表时间：
2016-05
影响因子：
1
通讯作者：
Pieter Belmans;Theo Raedschelders
中科院分区：
文献类型：
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作者：
Pieter Belmans;Theo Raedschelders
二次曲面的非对易变形通常用三维三次Artin-Schelter正则代数来描述。本文证明了对于这样一个代数，它的有界导范畴嵌入到二次曲面上两点的Hilbert格式的交换变形的有界导范畴中。这是支持奥尔洛夫猜想的第二个例子。基于这个例子，我们给出了这个猜想的一个无穷小版本，并在光滑射影曲面的情况下给出了一些证据。
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.