Global sections of square root line bundle The Next CEO of Stack OverflowGenerators of the ring of sections of a line bundleSimple example of an ample line bundle that is not very ampleExample for very ample line bundle numerically equivalent to a not very ample line bundleLine Bundle of deg 2g-1 and generated by global sectionsGlobal sections when we tensor by a degree zero line bundleGlobal sections of tensor powers of a line bundleAmple, Very ample line bundles on projective spaceObstructions for a root of a given line bundle on a curve over arbitrary base field to existDimension of global sections of an ample line bundle lower boundDoes the line bundle have global sections?
Multi tool use
Can Sri Krishna be called 'a person'?
Upgrading From a 9 Speed Sora Derailleur?
Compilation of a 2d array and a 1d array
What day is it again?
Why does freezing point matter when picking cooler ice packs?
How to unfasten electrical subpanel attached with ramset
Ising model simulation
Raspberry pi 3 B with Ubuntu 18.04 server arm64: what pi version
Early programmable calculators with RS-232
How to show a landlord what we have in savings?
Is there a rule of thumb for determining the amount one should accept for a settlement offer?
Another proof that dividing by 0 does not exist -- is it right?
Man transported from Alternate World into ours by a Neutrino Detector
Is this a new Fibonacci Identity?
pgfplots: How to draw a tangent graph below two others?
Can this transistor (2n2222) take 6V on emitter-base? Am I reading datasheet incorrectly?
Is a linearly independent set whose span is dense a Schauder basis?
The sum of any ten consecutive numbers from a fibonacci sequence is divisible by 11
Creating a script with console commands
That's an odd coin - I wonder why
What did the word "leisure" mean in late 18th Century usage?
Why do we say “un seul M” and not “une seule M” even though M is a “consonne”?
How can the PCs determine if an item is a phylactery?
"Eavesdropping" vs "Listen in on"
Global sections of square root line bundle
The Next CEO of Stack OverflowGenerators of the ring of sections of a line bundleSimple example of an ample line bundle that is not very ampleExample for very ample line bundle numerically equivalent to a not very ample line bundleLine Bundle of deg 2g-1 and generated by global sectionsGlobal sections when we tensor by a degree zero line bundleGlobal sections of tensor powers of a line bundleAmple, Very ample line bundles on projective spaceObstructions for a root of a given line bundle on a curve over arbitrary base field to existDimension of global sections of an ample line bundle lower boundDoes the line bundle have global sections?
$begingroup$
Let $C$ be a smooth curve in $mathbbP^2$ over field $mathbbC$. Suppose that I have a very ample line bundle $L$ on $C$ of even degree. Then $L$ has $2^2g$ square roots in $Pic C$. These are line bundles $A$ such that $Aotimes A=L$.
What can we say about $h^0(C,A)$? Is it non-empty for all $A$? Or is it possible that no such $A$ has sections?
algebraic-geometry algebraic-curves riemann-surfaces line-bundles
edited Mar 20 at 13:27
Stefano
2,223931
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
$endgroup$
add a comment |
$begingroup$
Let $C$ be a smooth curve in $mathbbP^2$ over field $mathbbC$. Suppose that I have a very ample line bundle $L$ on $C$ of even degree. Then $L$ has $2^2g$ square roots in $Pic C$. These are line bundles $A$ such that $Aotimes A=L$.
What can we say about $h^0(C,A)$? Is it non-empty for all $A$? Or is it possible that no such $A$ has sections?
algebraic-geometry algebraic-curves riemann-surfaces line-bundles
edited Mar 20 at 13:27
Stefano
2,223931
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
$endgroup$
add a comment |
$begingroup$
Let $C$ be a smooth curve in $mathbbP^2$ over field $mathbbC$. Suppose that I have a very ample line bundle $L$ on $C$ of even degree. Then $L$ has $2^2g$ square roots in $Pic C$. These are line bundles $A$ such that $Aotimes A=L$.
What can we say about $h^0(C,A)$? Is it non-empty for all $A$? Or is it possible that no such $A$ has sections?
algebraic-geometry algebraic-curves riemann-surfaces line-bundles
edited Mar 20 at 13:27
Stefano
2,223931
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
$endgroup$
Let $C$ be a smooth curve in $mathbbP^2$ over field $mathbbC$. Suppose that I have a very ample line bundle $L$ on $C$ of even degree. Then $L$ has $2^2g$ square roots in $Pic C$. These are line bundles $A$ such that $Aotimes A=L$.
What can we say about $h^0(C,A)$? Is it non-empty for all $A$? Or is it possible that no such $A$ has sections?
algebraic-geometry algebraic-curves riemann-surfaces line-bundles
algebraic-geometry algebraic-curves riemann-surfaces line-bundles
edited Mar 20 at 13:27
Stefano
2,223931
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
edited Mar 20 at 13:27
Stefano
2,223931
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
edited Mar 20 at 13:27
Stefano
2,223931
edited Mar 20 at 13:27
Stefano
2,223931
edited Mar 20 at 13:27
Stefano
2,223931
2,223931
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
asked Mar 20 at 9:28
gradstudentgradstudent
1,313720
1,313720
add a comment |
add a comment |
0
active
oldest
votes
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%2f3155203%2fglobal-sections-of-square-root-line-bundle%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
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%2f3155203%2fglobal-sections-of-square-root-line-bundle%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
qtgSoYi z0zZmgTppcni5a2xaz V1INRu4jpI Xw 7tfIkliq
