# MathSciDoc: An Archive for Mathematician ∫

#### Algebraic Geometrymathscidoc:1609.01006

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 \$\P^n\$ or quadric \$\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\$.
strictly nef bundle, projective space, quadrics
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