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arXiv · 1609.06867

Characterizations of projective spaces and quadrics by strictly nef bundles

Duo Li·Xiaokui Yang
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Abstract

In this paper, we show that if the tangent bundle of a smooth projective variety is strictly nef, then it is isomorphic to a projective space; if a projective variety $X^n$ $(n>4)$ has strictly nef $\Lambda^2 TX$, then it is isomorphic to $\mathbb{P}^n$ or quadric $\mathbb{Q}^n$. We also prove that on elliptic curves, strictly nef vector bundles are ample, whereas there exist Hermitian flat and strictly nef vector bundles on any smooth curve with genus $g\geq 2$.

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Duo Li, Xiaokui Yang. 2016-09-22. Characterizations of projective spaces and quadrics by strictly nef bundles. https://arxiv.org/abs/1609.06867

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