Critical Points of holomorphic sections of line bundles and a spherical Gauss-Lucas theorem

Jingzhou Sun

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arXiv · 1303.5349

Critical Points of holomorphic sections of line bundles and a spherical Gauss-Lucas theorem

Jingzhou Sun

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Abstract

We study critical points of holomorphic sections of $\ocal(m)$ on $\CP^n$. For quadrics, we give a complete discription of their critical points. When $n=1$, we prove a spherical Gauss-Lucas theorem. For general situation, we prove that a general section has all its critical points isolated and non-degenerate.

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Jingzhou Sun. 2013-03-21. Critical Points of holomorphic sections of line bundles and a spherical Gauss-Lucas theorem. https://arxiv.org/abs/1303.5349

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