Globally Generated Vector Bundle on a Riemann surface
$begingroup$
This is a very vague question, in fact not really a question at all more of a search.
I am studying some vector bundle theory on Riemann surfaces and would just like some non-trivial example of globally generated complex vector bundles of rank greater than one.
Does anybody have some examples which arise naturally in complex(& algebraic) geometry or topology?
differential-geometry algebraic-geometry complex-geometry vector-bundles riemann-surfaces
edited Dec 8 '18 at 13:25
Armando j18eos
2,63511328
asked Dec 6 '18 at 10:23
benben
113
$endgroup$
add a comment |
$begingroup$
This is a very vague question, in fact not really a question at all more of a search.
I am studying some vector bundle theory on Riemann surfaces and would just like some non-trivial example of globally generated complex vector bundles of rank greater than one.
Does anybody have some examples which arise naturally in complex(& algebraic) geometry or topology?
differential-geometry algebraic-geometry complex-geometry vector-bundles riemann-surfaces
edited Dec 8 '18 at 13:25
Armando j18eos
2,63511328
asked Dec 6 '18 at 10:23
benben
113
$endgroup$
add a comment |
$begingroup$
This is a very vague question, in fact not really a question at all more of a search.
I am studying some vector bundle theory on Riemann surfaces and would just like some non-trivial example of globally generated complex vector bundles of rank greater than one.
Does anybody have some examples which arise naturally in complex(& algebraic) geometry or topology?
differential-geometry algebraic-geometry complex-geometry vector-bundles riemann-surfaces
edited Dec 8 '18 at 13:25
Armando j18eos
2,63511328
asked Dec 6 '18 at 10:23
benben
113
$endgroup$
This is a very vague question, in fact not really a question at all more of a search.
I am studying some vector bundle theory on Riemann surfaces and would just like some non-trivial example of globally generated complex vector bundles of rank greater than one.
Does anybody have some examples which arise naturally in complex(& algebraic) geometry or topology?
differential-geometry algebraic-geometry complex-geometry vector-bundles riemann-surfaces
differential-geometry algebraic-geometry complex-geometry vector-bundles riemann-surfaces
edited Dec 8 '18 at 13:25
Armando j18eos
2,63511328
asked Dec 6 '18 at 10:23
benben
113
edited Dec 8 '18 at 13:25
Armando j18eos
2,63511328
asked Dec 6 '18 at 10:23
benben
113
edited Dec 8 '18 at 13:25
Armando j18eos
2,63511328
edited Dec 8 '18 at 13:25
Armando j18eos
2,63511328
edited Dec 8 '18 at 13:25
Armando j18eos
2,63511328
2,63511328
asked Dec 6 '18 at 10:23
benben
113
asked Dec 6 '18 at 10:23
benben
113
asked Dec 6 '18 at 10:23
benben
113
113
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
If $C subset mathbb{P}^n$ is a projective embedding of a Riemann surface, the normal bundle
$$
N_{C/mathbb{P}^n}
$$
is globally generated of rank $n-1$.
answered Dec 6 '18 at 10:44
SashaSasha
4,898139
$endgroup$
$begingroup$
Thank you for the response! This is the only interesting example I was aware of, I should have mentioned this in the post.
$endgroup$
– ben
Dec 7 '18 at 12:24
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
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%2fmath.stackexchange.com%2fquestions%2f3028312%2fglobally-generated-vector-bundle-on-a-riemann-surface%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If $C subset mathbb{P}^n$ is a projective embedding of a Riemann surface, the normal bundle
$$
N_{C/mathbb{P}^n}
$$
is globally generated of rank $n-1$.
answered Dec 6 '18 at 10:44
SashaSasha
4,898139
$endgroup$
$begingroup$
Thank you for the response! This is the only interesting example I was aware of, I should have mentioned this in the post.
$endgroup$
– ben
Dec 7 '18 at 12:24
add a comment |
$begingroup$
If $C subset mathbb{P}^n$ is a projective embedding of a Riemann surface, the normal bundle
$$
N_{C/mathbb{P}^n}
$$
is globally generated of rank $n-1$.
answered Dec 6 '18 at 10:44
SashaSasha
4,898139
$endgroup$
$begingroup$
Thank you for the response! This is the only interesting example I was aware of, I should have mentioned this in the post.
$endgroup$
– ben
Dec 7 '18 at 12:24
add a comment |
$begingroup$
If $C subset mathbb{P}^n$ is a projective embedding of a Riemann surface, the normal bundle
$$
N_{C/mathbb{P}^n}
$$
is globally generated of rank $n-1$.
answered Dec 6 '18 at 10:44
SashaSasha
4,898139
$endgroup$
If $C subset mathbb{P}^n$ is a projective embedding of a Riemann surface, the normal bundle
$$
N_{C/mathbb{P}^n}
$$
is globally generated of rank $n-1$.
answered Dec 6 '18 at 10:44
SashaSasha
4,898139
answered Dec 6 '18 at 10:44
SashaSasha
4,898139
answered Dec 6 '18 at 10:44
SashaSasha
4,898139
answered Dec 6 '18 at 10:44
SashaSasha
4,898139
4,898139
$begingroup$
Thank you for the response! This is the only interesting example I was aware of, I should have mentioned this in the post.
$endgroup$
– ben
Dec 7 '18 at 12:24
add a comment |
$begingroup$
Thank you for the response! This is the only interesting example I was aware of, I should have mentioned this in the post.
$endgroup$
– ben
Dec 7 '18 at 12:24
$begingroup$
Thank you for the response! This is the only interesting example I was aware of, I should have mentioned this in the post.
$endgroup$
– ben
Dec 7 '18 at 12:24
$begingroup$
Thank you for the response! This is the only interesting example I was aware of, I should have mentioned this in the post.
$endgroup$
– ben
Dec 7 '18 at 12:24
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- 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.
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%2fmath.stackexchange.com%2fquestions%2f3028312%2fglobally-generated-vector-bundle-on-a-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
