Bigness of tangent bundles and dynamical rigidity of Fano manifolds of Picard number 1 (with an appendix by Jie Liu)

2023/11/27 by Shao, Feng, Zhong, Guolei
#14J40 #14J45 #Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.15559

Abstract

Let f\colon X→ Y be a surjective morphism of Fano manifolds of Picard number 1 whose VMRTs at a general point are not dual defective. Suppose that the tangent bundle T_X is big. We show that f is an isomorphism unless Y is a projective space. As applications, we study the bigness of the tangent bundles of complete intersections, del Pezzo manifolds, and Mukai manifolds, as well as their dynamical rigidity.

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