Lefschetz exceptional collections in S_k-equivariant categories of\n (\ℙⁿ)^k

2018/07/04 by Mikhail Mironov, Mironov, Mikhail
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1807.01534

openalex publication_date 2018/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the bounded derived category of S_k-equivariant coherent\nsheaves on (\ℙⁿ)^k. The goal of this paper is to construct in this\ncategory a rectangular Lefschetz exceptional collection when this is possible,\nor a minimal Lefschetz exceptional collection when a rectangular one does not\nexist. The main results of the paper include the construction of a rectangular\nLefschetz exceptional collection in the case k=3 and in the case n=1 when\ngcd(n+1,k)=1. We also construct minimal Lefschetz exceptional\ncollection for n=1 and even k, and for n=2 and k=3.\n

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