In 1970, Kobayashi conjectured that general hypersurfaces of sufficiently large degree in \(\mathbf {P}^{n}\) are hyperbolic. In this paper we prove that a general sufficiently ample hypersurface in a smooth projective variety is hyperbolic. To prove this statement, we construct hypersurfaces satisfying a property which is Zariski open and which implies hyperbolicity. These hypersurfaces are chosen such that the geometry of their higher order jet spaces can be related to the geometry of a universal family of complete intersections. To do so, we introduce a Wronskian construction which associates a (twisted) jet differential to every finite family of global sections of a line bundle.

中文翻译：

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关于一般超曲面的双曲性

1970年，小林博士推测\（\ mathbf {P} ^ {n} \）中足够大的一般超曲面是双曲线的。在本文中，我们证明了光滑射影中一般足够充分的超曲面是双曲线的。为了证明这一说法，我们构造了满足Zariski开放性质和暗示双曲性质的超曲面。选择这些超曲面，以便其高阶射流空间的几何形状可以与完整相交的通用族的几何形状相关。为此，我们引入了Wronskian构造，该构造将（扭曲的）射流差速器与线束的全局部分的每个有限族相关联。