The cotangent bundle of a non-compact Riemann surface
up vote
2
down vote
favorite
Suppose that $M$ is a non-compact Riemann surface obtained by removing several points from a compact one. It is known that the holomorphic cotangent bundle of $M$ is trivial. Therefore there exists a holomorphic 1-form $omega$ that does not have any zeroes on $M$. I am interested to know whether we can find an exact 1-form $omega=df$, where $f$ is some holomorphic function on $M$, such that $omega$ does not have zeroes on $M$.
ag.algebraic-geometry
asked 3 hours ago
Todor
361
add a comment |
up vote
2
down vote
favorite
Suppose that $M$ is a non-compact Riemann surface obtained by removing several points from a compact one. It is known that the holomorphic cotangent bundle of $M$ is trivial. Therefore there exists a holomorphic 1-form $omega$ that does not have any zeroes on $M$. I am interested to know whether we can find an exact 1-form $omega=df$, where $f$ is some holomorphic function on $M$, such that $omega$ does not have zeroes on $M$.
ag.algebraic-geometry
asked 3 hours ago
Todor
361
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
Suppose that $M$ is a non-compact Riemann surface obtained by removing several points from a compact one. It is known that the holomorphic cotangent bundle of $M$ is trivial. Therefore there exists a holomorphic 1-form $omega$ that does not have any zeroes on $M$. I am interested to know whether we can find an exact 1-form $omega=df$, where $f$ is some holomorphic function on $M$, such that $omega$ does not have zeroes on $M$.
ag.algebraic-geometry
asked 3 hours ago
Todor
361
Suppose that $M$ is a non-compact Riemann surface obtained by removing several points from a compact one. It is known that the holomorphic cotangent bundle of $M$ is trivial. Therefore there exists a holomorphic 1-form $omega$ that does not have any zeroes on $M$. I am interested to know whether we can find an exact 1-form $omega=df$, where $f$ is some holomorphic function on $M$, such that $omega$ does not have zeroes on $M$.
ag.algebraic-geometry
ag.algebraic-geometry
asked 3 hours ago
Todor
361
asked 3 hours ago
Todor
361
asked 3 hours ago
Todor
361
asked 3 hours ago
Todor
361
asked 3 hours ago
Todor
361
361
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
3
down vote
Such $f$ exists on any open Riemann surface:
R.C. Gunning and R. Narasimhan. Immersion of open Riemann surfaces.
Math. Ann., 174:103–108, 1967.
answered 2 hours ago
Alexandre Eremenko
48.5k6134250
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
Such $f$ exists on any open Riemann surface:
R.C. Gunning and R. Narasimhan. Immersion of open Riemann surfaces.
Math. Ann., 174:103–108, 1967.
answered 2 hours ago
Alexandre Eremenko
48.5k6134250
add a comment |
up vote
3
down vote
Such $f$ exists on any open Riemann surface:
R.C. Gunning and R. Narasimhan. Immersion of open Riemann surfaces.
Math. Ann., 174:103–108, 1967.
answered 2 hours ago
Alexandre Eremenko
48.5k6134250
add a comment |
up vote
3
down vote
up vote
3
down vote
Such $f$ exists on any open Riemann surface:
R.C. Gunning and R. Narasimhan. Immersion of open Riemann surfaces.
Math. Ann., 174:103–108, 1967.
answered 2 hours ago
Alexandre Eremenko
48.5k6134250
Such $f$ exists on any open Riemann surface:
R.C. Gunning and R. Narasimhan. Immersion of open Riemann surfaces.
Math. Ann., 174:103–108, 1967.
answered 2 hours ago
Alexandre Eremenko
48.5k6134250
answered 2 hours ago
Alexandre Eremenko
48.5k6134250
answered 2 hours ago
Alexandre Eremenko
48.5k6134250
answered 2 hours ago
Alexandre Eremenko
48.5k6134250
48.5k6134250
add a comment |
add a comment |
Thanks for contributing an answer to MathOverflow!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathoverflow.net%2fquestions%2f316925%2fthe-cotangent-bundle-of-a-non-compact-riemann-surface%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
