A Horrocks' theorem for reflexive sheaves

2017/12/05 by Costa, Laura, Marchesi, Simone, Miró-Roig, Rosa Maria
#14F05 #14J60 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1712.01528

Abstract

In this paper, we define m-tail reflexive sheaves as reflexive sheaves on projective spaces with the simplest possible cohomology. We prove that the rank of any m-tail reflexive sheaf E on Pⁿ is greater or equal to nm-m. We completely describe m-tail reflexive sheaves on Pⁿ of minimal rank and we construct huge families of m-tail reflexive sheaves of higher rank.

Related

• The Cohomology of Reflexive Sheaves on Smooth Projective 3-folds
• Moduli of Reflexive Sheaves on Smooth Projective 3-folds
• Rank two sheaves with maximal third Chern character in three-dimensional\n projective space
• Lazarsfeld-Mukai Reflexive Sheaves and their Stability
• Splitting criterion for reflexive sheaves