List questions from several-complex-variables

Published on 22 Mar 2026 - 15:42

92

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Show the set is closed

Published on 21 Mar 2026 - 18:52

75

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Show the zero set of a holomorphic section can be written as the union of two disjoint closed set

Published on 21 Mar 2026 - 16:21

68

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Differential of logarithm on complex plane

Published on 22 Mar 2026 - 5:05

817

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Does every non-compact Riemann surface embed holomorphically into $\mathbb{C}^2$?

Published on 25 Mar 2026 - 1:25

75

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Is there a by-hand prove that $\Gamma(\mathbb{C}P^n,E)$ is finite dimensional for a holomorphic vector bundle $E$?

Published on 22 Mar 2026 - 4:28

249

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Holomorphic Morse functions

Published on 21 Mar 2026 - 22:45

59

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If function has a zero on an open set, then it has a zero on the boundary

Published on 21 Mar 2026 - 18:35

199

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Links between several complex variables and number theory?

Published on 22 Mar 2026 - 2:25

46

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Finding a holomorphic function

Published on 22 Mar 2026 - 15:56

21

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Maximum co-dimension of a submanifold given by finitely many holomorphic functions

Published on 25 Mar 2026 - 1:31

66

Views

Holomorphic morphism sending given curves to give points

Published on 21 Mar 2026 - 19:16

173

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Holomorphic morphisms cannot be extended to codimension $2$

Published on 22 Mar 2026 - 9:53

77

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Visual representation for a function $f:\left(\mathbb{C}^2\right)^2\to\left(\mathbb{C}^2\right)^2$

Published on 22 Mar 2026 - 5:44

55

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On a sufficient condition for being a prime ideal

Published on 22 Mar 2026 - 0:15

List Question

Analytic proof that infinite level sets of complex polynomials aren't compact

Show the set is closed

Show the zero set of a holomorphic section can be written as the union of two disjoint closed set

Differential of logarithm on complex plane

Does every non-compact Riemann surface embed holomorphically into $\mathbb{C}^2$?

Is there a by-hand prove that $\Gamma(\mathbb{C}P^n,E)$ is finite dimensional for a holomorphic vector bundle $E$?

Holomorphic Morse functions

If function has a zero on an open set, then it has a zero on the boundary

Links between several complex variables and number theory?

Finding a holomorphic function

Maximum co-dimension of a submanifold given by finitely many holomorphic functions

Holomorphic morphism sending given curves to give points

Holomorphic morphisms cannot be extended to codimension $2$

Visual representation for a function $f:\left(\mathbb{C}^2\right)^2\to\left(\mathbb{C}^2\right)^2$

On a sufficient condition for being a prime ideal

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