Fano manifolds with big tangent bundle: a characterisation of $V_5$

TL;DR

This paper characterizes the Fano manifold V_5 by showing that if a Fano manifold with Picard number one has a big tangent bundle and admits a rational curve with trivial normal bundle, then it is isomorphic to V_5.

Contribution

It provides a new characterization of V_5 among Fano manifolds with big tangent bundle and specific rational curves.

Findings

X is isomorphic to V_5 under given conditions

Big tangent bundle implies special geometric properties

Existence of a rational curve with trivial normal bundle is crucial

Abstract

Let X be a Fano manifold with Picard number one such that the tangent bundle T_X is big. If X admits a rational curve with trivial normal bundle, we show that X is isomorphic to the del Pezzo threefold of degree five.