Fano 5-folds with nef tangent bundles and Picard numbers greater than one

2012/08/16 by Kiwamu Watanabe, Watanabe, Kiwamu
Mathematics · #14J40 #14J45 #14M17 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #math.AG #msc:14J40 #msc:14J45 #msc:14M17

paper · pdf · doi:10.48550/arxiv.1208.3302

12 pages, corrected some errors, to appear in Math. Z

openalex publication_date 2012/08/16 · arxiv created 2013/04/09 · arxiv updated 2013/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that smooth Fano 5-folds with nef tangent bundles and Picard numbers greater than one are rational homogeneous manifolds.

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• Fano n-folds with nef tangent bundle and Picard number greater than n-5
• Fano 5-folds with nef tangent bundles
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• Fano manifolds of coindex three admitting nef tangent bundle