Fullness of the Kuznetsov–Polishchuk Exceptional Collection for the Spinor Tenfold

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2023-12-28 DOI:10.1007/s10468-023-10246-6

Riccardo Moschetti, Marco Rampazzo

引用次数: 0

Abstract

Kuznetsov and Polishchuk provided a general algorithm to construct exceptional collections of maximal length for homogeneous varieties of type A, B, C, D. We consider the case of the spinor tenfold and we prove that the corresponding collection is full, i.e. it generates the whole derived category of coherent sheaves. We also verify strongness and purity of such collection. As a step of the proof, we construct some resolutions of homogeneous vector bundles which might be of independent interest.

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库兹涅佐夫-波利什丘克旋转体十倍异常集合的丰满度

库兹涅佐夫（Kuznetsov）和波兰丘克（Polishchuk）为 A、B、C、D 型同质变体构建最大长度的特殊集合提供了一种通用算法。我们考虑了旋量十重的情况，并证明了相应的集合是完整的，即它产生了整个相干剪切的派生范畴。我们还验证了这种集合的强性和纯粹性。作为证明的一个步骤，我们构建了一些同质向量束的解析，这些解析可能会引起我们的兴趣。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.