On holomorphic distributions on Fano threefolds

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Cavalcante, Alana¹  Correa, Mauricio²  Marchesi, Simone³ 

[1] UFOP, R Trinta & Seis 115, BR-35931008 Joao Monlevade, Brazil

[2] Univ Fed Minas Gerais, Ave Antonio Carlos 6627, BR-30161970 Belo Horizonte, MG, Brazil

[3] Univ Barcelona, Gran Via de les Corts Catalanes 585, E-08007 Barcelona, Spain

关键词: Holomorphic distributions;    Fano manifolds;    Split vector bundles;    Stable vector bundles;   

DOI  :  10.1016/j.jpaa.2019.106272

来源: Elsevier

【 摘 要 】

This paper is devoted to the study of holomorphic distributions of dimension and codimension one on smooth weighted projective complete intersection Fano manifolds X which is threedimensional and with Picard number equal to one. We study the relations between algebro-geometric properties of the singular set of singular holomorphic distributions and their associated sheaves. We characterize either distributions whose tangent sheaf or conormal sheaf are arithmetically Cohen Macaulay (aCM) on X. We also prove that a codimension one locally free distribution with trivial canonical bundle on any Fano threefold, with Picard number equal to one, has a tangent sheaf which either splits or it is stable. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free