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arXiv · 2311.15559

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

Feng Shao·Guolei Zhong
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Abstract

Let $f\colon X\to Y$ 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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Feng Shao, Guolei Zhong. 2023-11-27. Bigness of tangent bundles and dynamical rigidity of Fano manifolds of Picard number 1 (with an appendix by Jie Liu). https://arxiv.org/abs/2311.15559

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