Question

For genus $g$ Riemann surface, $\operatorname{H}^1(X)$ has complex dimension $2g$?

score 217 · Answer 1 · 2018-06-02 08:03:26

217

Views

For genus $g$ Riemann surface, $\operatorname{H}^1(X)$ has complex dimension $2g$?

Published on 02 Jun 2018 - 8:03

score 95 · Answer 2 · 2018-06-02 08:15:30

95

Views

If $X$ is a Riemann surface, does $T_p^*X$ have complex dimension $1$ or $2$?

Published on 02 Jun 2018 - 8:15

score 121 · Answer 3 · 2018-06-05 00:28:59

121

Views

What does "The map g be geometrically interpreted as the stereographic projection of the Gauss map" mean?

Published on 05 Jun 2018 - 0:28

score 60 · Answer 4 · 2018-06-08 06:50:25

60

Views

How to show the $\overline{P_{1}P_{2}}$ intersect $y^2=f(x)=4x^3-g_{2}x-g_{3}$ is $P_{3}=(p(z_{1}+z_{2}),-p'(z_{1}+z_{2}))$

Published on 08 Jun 2018 - 6:50

score 490 · Answer 5 · 2018-06-09 05:56:38

490

Views

Square root of even degree line bundle

Published on 09 Jun 2018 - 5:56

score 86 · Answer 6 · 2018-06-09 10:10:29

86

Views

Sphere minus interval is upper half plane $\mathbb{C}_{\infty} - [a \ , b] \simeq \mathcal{H}$?

Published on 09 Jun 2018 - 10:10

score 330 · Answer 7 · 2018-06-09 22:11:23

330

Views

Why is the composition of convergent Laurent series convergent?

Published on 09 Jun 2018 - 22:11

score 384 · Answer 8 · 2018-06-15 20:19:37

384

Views

Convergence of harmonic functions in $L^1_{loc}$ implies uniform convergence on compact subsets

Published on 15 Jun 2018 - 20:19

score 96 · Answer 9 · 2018-06-20 05:50:50

96

Views

Show that any harmonic map $f:\Sigma_1 \rightarrow \Sigma_2$ is a constant.

Published on 20 Jun 2018 - 5:50

score 281 · Answer 10 · 2018-06-20 07:29:25

281

Views

Convex function on geodesics in hyperbolic plane

Published on 20 Jun 2018 - 7:29

score 234 · Answer 11 · 2018-06-20 21:06:19

234

Views

Cyclic Cover of the Projective Line

Published on 20 Jun 2018 - 21:06

score 413 · Answer 12 · 2018-06-28 10:56:31

413

Views

Questions on cyclic covers of the projective line

Published on 28 Jun 2018 - 10:56

score 385 · Answer 13 · 2018-07-01 07:33:43

385

Views

degree of line bundle as an integral

Published on 01 Jul 2018 - 7:33

score 39 · Answer 14 · 2018-07-04 03:58:27

39

Views

Belyi function : degree of pole is the degree of the face - why?

Published on 04 Jul 2018 - 3:58

score 1.3k · Answer 15 · 2026-03-23 00:55:06

1.3k

Views

What is the real and imaginary part of complex infinity?

Published on 23 Mar 2026 - 0:55

List Question

For genus $g$ Riemann surface, $\operatorname{H}^1(X)$ has complex dimension $2g$?

If $X$ is a Riemann surface, does $T_p^*X$ have complex dimension $1$ or $2$?

What does "The map g be geometrically interpreted as the stereographic projection of the Gauss map" mean?

How to show the $\overline{P_{1}P_{2}}$ intersect $y^2=f(x)=4x^3-g_{2}x-g_{3}$ is $P_{3}=(p(z_{1}+z_{2}),-p'(z_{1}+z_{2}))$

Square root of even degree line bundle

Sphere minus interval is upper half plane $\mathbb{C}_{\infty} - [a \ , b] \simeq \mathcal{H}$?

Why is the composition of convergent Laurent series convergent?

Convergence of harmonic functions in $L^1_{loc}$ implies uniform convergence on compact subsets

Show that any harmonic map $f:\Sigma_1 \rightarrow \Sigma_2$ is a constant.

Convex function on geodesics in hyperbolic plane

Cyclic Cover of the Projective Line

Questions on cyclic covers of the projective line

degree of line bundle as an integral

Belyi function : degree of pole is the degree of the face - why?

What is the real and imaginary part of complex infinity?

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