Is every analytic hypersurface in $\mathbb{C}^n$ cut out by one holomorphic function?
2026-03-29 21:51:44.1774821104
Is every analytic hypersurface in $\mathbb{C}^n$ cut out by one holomorphic function?
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Yes; this follows from $H^1(\mathbf C^n, \mathcal O^\times)=0$. See Griffiths & Harris, Chapter 0, Section 3 (p. 47 in my edition).