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Critical Points of holomorphic sections of line bundles and a spherical Gauss-Lucas theorem
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math.CVmath.DG
keywords
criticalpointsgauss-lucasgeneralholomorphicprovesectionsspherical
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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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