Cartier divisor $mathbb{Q}$-trivial
5
$begingroup$
Let $X$ be a projective variety and $D$ a Cartier divisor on $X$ so that $Dsim_mathbb{Q} 0$. Is it true that $D$ is itself linearly equivalent to zero?
algebraic-geometry commutative-algebra
asked Dec 27 '18 at 23:02
WeiWei
311
$endgroup$
add a comment |
5
$begingroup$
Let $X$ be a projective variety and $D$ a Cartier divisor on $X$ so that $Dsim_mathbb{Q} 0$. Is it true that $D$ is itself linearly equivalent to zero?
algebraic-geometry commutative-algebra
asked Dec 27 '18 at 23:02
WeiWei
311
$endgroup$
$begingroup$
Welcome the Mathematics Stack Exchange! A quick tour of the site (math.stackexchange.com/tour) will help you get the most of your time here.
$endgroup$
– dantopa
Dec 27 '18 at 23:09
3
$begingroup$
I'm not very familiar with the notion of Q rational Cartier divisors, but it seems like a nontrivial Cartier divisor D which is torsion in the Cartier class group should provide a counterexample, right?
$endgroup$
– Stahl
Dec 27 '18 at 23:56
add a comment |
5
5
5
$begingroup$
Let $X$ be a projective variety and $D$ a Cartier divisor on $X$ so that $Dsim_mathbb{Q} 0$. Is it true that $D$ is itself linearly equivalent to zero?
algebraic-geometry commutative-algebra
asked Dec 27 '18 at 23:02
WeiWei
311
$endgroup$
Let $X$ be a projective variety and $D$ a Cartier divisor on $X$ so that $Dsim_mathbb{Q} 0$. Is it true that $D$ is itself linearly equivalent to zero?
algebraic-geometry commutative-algebra
algebraic-geometry commutative-algebra
asked Dec 27 '18 at 23:02
WeiWei
311
asked Dec 27 '18 at 23:02
WeiWei
311
asked Dec 27 '18 at 23:02
WeiWei
311
asked Dec 27 '18 at 23:02
WeiWei
311
asked Dec 27 '18 at 23:02
WeiWei
311
311
$begingroup$
Welcome the Mathematics Stack Exchange! A quick tour of the site (math.stackexchange.com/tour) will help you get the most of your time here.
$endgroup$
– dantopa
Dec 27 '18 at 23:09
3
$begingroup$
I'm not very familiar with the notion of Q rational Cartier divisors, but it seems like a nontrivial Cartier divisor D which is torsion in the Cartier class group should provide a counterexample, right?
$endgroup$
– Stahl
Dec 27 '18 at 23:56
add a comment |
$begingroup$
Welcome the Mathematics Stack Exchange! A quick tour of the site (math.stackexchange.com/tour) will help you get the most of your time here.
$endgroup$
– dantopa
Dec 27 '18 at 23:09
3
$begingroup$
I'm not very familiar with the notion of Q rational Cartier divisors, but it seems like a nontrivial Cartier divisor D which is torsion in the Cartier class group should provide a counterexample, right?
$endgroup$
– Stahl
Dec 27 '18 at 23:56
$begingroup$
Welcome the Mathematics Stack Exchange! A quick tour of the site (math.stackexchange.com/tour) will help you get the most of your time here.
$endgroup$
– dantopa
Dec 27 '18 at 23:09
$begingroup$
Welcome the Mathematics Stack Exchange! A quick tour of the site (math.stackexchange.com/tour) will help you get the most of your time here.
$endgroup$
– dantopa
Dec 27 '18 at 23:09
3
3
$begingroup$
I'm not very familiar with the notion of Q rational Cartier divisors, but it seems like a nontrivial Cartier divisor D which is torsion in the Cartier class group should provide a counterexample, right?
$endgroup$
– Stahl
Dec 27 '18 at 23:56
$begingroup$
I'm not very familiar with the notion of Q rational Cartier divisors, but it seems like a nontrivial Cartier divisor D which is torsion in the Cartier class group should provide a counterexample, right?
$endgroup$
– Stahl
Dec 27 '18 at 23:56
add a comment |
0
active
oldest
votes
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
});
}
});
draft saved
draft discarded
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%2f3054427%2fcartier-divisor-mathbbq-trivial%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
draft saved
draft discarded
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.
draft saved
draft discarded
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%2f3054427%2fcartier-divisor-mathbbq-trivial%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
$begingroup$
Welcome the Mathematics Stack Exchange! A quick tour of the site (math.stackexchange.com/tour) will help you get the most of your time here.
$endgroup$
– dantopa
Dec 27 '18 at 23:09
3
$begingroup$
I'm not very familiar with the notion of Q rational Cartier divisors, but it seems like a nontrivial Cartier divisor D which is torsion in the Cartier class group should provide a counterexample, right?
$endgroup$
– Stahl
Dec 27 '18 at 23:56