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<p>In this paper, we develop the techniques of slanted vector fields, especially the techniques of partial slanted vector fields, to apply them to Wronskian-type holomorphic <i>n</i>-jet differentials on the <i>n</i>-dimensional complex hypersurface in the projective space constructed by Cramer’s rule, to prove the hyperbolicity of generic <i>n</i>-dimensional complex hypersurfaces of degree greater than or equal to 49<i>n</i><sup>2</sup> in the projective space.</p>

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Hyperbolicity of generic hypersurface in ℙn+1 of degree at least 49n2

  • 期刊论文

  • 发表日期：

    2026年5月28日

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  • Yum-Tong Siu

摘要

In this paper, we develop the techniques of slanted vector fields, especially the techniques of partial slanted vector fields, to apply them to Wronskian-type holomorphic n-jet differentials on the n-dimensional complex hypersurface in the projective space constructed by Cramer’s rule, to prove the hyperbolicity of generic n-dimensional complex hypersurfaces of degree greater than or equal to 49n2 in the projective space.