An abundance-type result for the tangent bundles of smooth Fano varieties

2024/08/07 by Wang, Juanyong
#14E30 #14J45 #14M17 #32J27 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.03799

Abstract

In this paper we prove the following abundance-type result: for any smooth Fano variety X, the tangent bundle T_X is nef if and only if it is big and semiample in the sense that the tautological line bundle \mathscrO_ℙTX(1) is so, by which we establish a weak form of the Campana-Peternell conjecture (Camapan-Peternell, 1991).

Related

• Fano 4-folds with nef tangent bundle in positive characteristic
• Positivity of the exterior power of the tangent bundles
• Toric Fano manifolds with nef tangent bundles
• Extremal rays and nefness of tangent bundles
• Balanced line bundles on Fano varieties