The cotangent bundle of a non-compact Riemann surface
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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
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Todor
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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 2 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 2 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 2 hours ago
Todor
361
asked 2 hours ago
Todor
361
asked 2 hours ago
Todor
361
asked 2 hours ago
Todor
361
asked 2 hours ago
Todor
361
361
add a comment |
add a comment |
1 Answer
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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
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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 |
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