Examples of rank two aCM bundles on smooth quartic surfaces in ℙ³

2016/01/12 by Gianfranco Casnati, Casnati, Gianfranco, Roberto Notari +1
Mathematics · #14J45 (Secondary) #14J60 (Primary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1601.02907

openalex publication_date 2016/01/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let F⊆ℙ³ be a smooth quartic surface and let O_F(h):=O_ℙ³(1)\otimesO_F. In the present paper we classify locally free sheaves E of rank 2 on F such that c₁(E)=O_F(2h), c₂(E)=8 and h¹(F,E(th))=0 for t∈ℤ. We also deal with their stability.

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