Question

Why is the set of points in $\mathbb{C}P^2$ where a non-degenerated quadratic form vanishes biholomorphic to $\mathbb{C}P^1$?

score 20 · Answer 1 · 2026-03-25 22:05:07

20

Views

Why is the set of points in $\mathbb{C}P^2$ where a non-degenerated quadratic form vanishes biholomorphic to $\mathbb{C}P^1$?

Published on 25 Mar 2026 - 22:05

score 56 · Answer 2 · 2026-03-25 19:05:45

56

Views

Calculating the difference between $f(x+iy)$ and $f(x-iy)$ when $y\to0+$

Published on 25 Mar 2026 - 19:05

score 122 · Answer 3 · 2026-03-25 09:48:12

122

Views

Why is conformal mapping important for Riemann Sphere

Published on 25 Mar 2026 - 9:48

score 40 · Answer 4 · 2026-03-25 09:26:21

40

Views

Prove Stereographic projection is a homeomorphism from Sphere except North Pole to Complex Plane

Published on 25 Mar 2026 - 9:26

score 32 · Answer 5 · 2026-03-26 19:18:25

32

Views

Curl of normal unit vector of a smooth and closed surface?

Published on 26 Mar 2026 - 19:18

score 88 · Answer 6 · 2023-10-14 01:59:47

88

Views

Formula for gaussian curvature of a holomorphic curve in complex 2-space

Published on 14 Oct 2023 - 1:59

score 36 · Answer 7 · 2023-10-21 16:45:04

36

Views

$\bar{S}=\left\{[z,w,t]\in \mathbb{C}P^2 : w^2t^{k-2}=(z-a_1t)\ldots (z-a_kt)\right\}$ is a Riemann surface iff $k \leq 3$

Published on 21 Oct 2023 - 16:45

score 123 · Answer 8 · 2023-10-23 09:54:04

123

Views

Checking that a differential form is holomorphic on an algebraic curve and that it extends to a holomorphic form on its compactification

Published on 23 Oct 2023 - 9:54

score 53 · Answer 9 · 2026-03-26 07:35:23

53

Views

If the degree of a divisor on a Riemann surface is $\deg(D) \geq 2g$, then $L(D-(p)) \subsetneq L(D)$ for any point $p$

Published on 26 Mar 2026 - 7:35

score 48 · Answer 10 · 2023-11-02 12:30:21

48

Views

Are rational functions on the Riemann sphere invariantly characterized? If so, what about general Riemann surfaces?

Published on 02 Nov 2023 - 12:30

score 66 · Answer 11 · 2023-11-02 16:56:28

66

Views

About Galois branched covers of Riemann Surfaces

Published on 02 Nov 2023 - 16:56

score 12 · Answer 12 · 2026-03-28 15:29:29

12

Views

Smooth part of an Affine Plane Curve defined by irreducible polynomial is a Riemann Surface

Published on 28 Mar 2026 - 15:29

score 77 · Answer 13 · 2023-11-06 02:31:29

77

Views

Evaluate function at $\infty$ in $\mathbb{C}^\infty$

Published on 06 Nov 2023 - 2:31

score 54 · Answer 14 · 2026-03-25 23:36:25

54

Views

Möbius transformation taking line segment between two complex numbers to the segment $[-1,1]$

Published on 25 Mar 2026 - 23:36

score 703 · Answer 15 · 2026-03-26 17:32:46

703

Views

Description of Riemann surface of polynomial inverse

Published on 26 Mar 2026 - 17:32

List Question

Why is the set of points in $\mathbb{C}P^2$ where a non-degenerated quadratic form vanishes biholomorphic to $\mathbb{C}P^1$?

Calculating the difference between $f(x+iy)$ and $f(x-iy)$ when $y\to0+$

Why is conformal mapping important for Riemann Sphere

Prove Stereographic projection is a homeomorphism from Sphere except North Pole to Complex Plane

Curl of normal unit vector of a smooth and closed surface?

Formula for gaussian curvature of a holomorphic curve in complex 2-space

$\bar{S}=\left\{[z,w,t]\in \mathbb{C}P^2 : w^2t^{k-2}=(z-a_1t)\ldots (z-a_kt)\right\}$ is a Riemann surface iff $k \leq 3$

Checking that a differential form is holomorphic on an algebraic curve and that it extends to a holomorphic form on its compactification

If the degree of a divisor on a Riemann surface is $\deg(D) \geq 2g$, then $L(D-(p)) \subsetneq L(D)$ for any point $p$

Are rational functions on the Riemann sphere invariantly characterized? If so, what about general Riemann surfaces?

About Galois branched covers of Riemann Surfaces

Smooth part of an Affine Plane Curve defined by irreducible polynomial is a Riemann Surface

Evaluate function at $\infty$ in $\mathbb{C}^\infty$

Möbius transformation taking line segment between two complex numbers to the segment $[-1,1]$

Description of Riemann surface of polynomial inverse

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