Projective subvarieties of a quasiprojective varietyWhy are torsion points dense in an abelian variety?Why can't subvarieties separate?Products of Ideal Sheaves and Union of irreducible SubvarietiesAccumulation of algebraic subvarieties: Near one subvariety there are many others (?), 2How should the degree of a variety be defined in a weighted projective space?Valuations given by flags on a variety and valuations of maximal rational rankLocus of complete curves on $mathcal M_g$What is the expected dimension of the Zariski closure of the rational points on the moduli space of curves?Motivic fundamental group of the moduli space of curves?How to calculate tautological classes of some varieties?
Projective subvarieties of a quasiprojective variety
Why are torsion points dense in an abelian variety?Why can't subvarieties separate?Products of Ideal Sheaves and Union of irreducible SubvarietiesAccumulation of algebraic subvarieties: Near one subvariety there are many others (?), 2How should the degree of a variety be defined in a weighted projective space?Valuations given by flags on a variety and valuations of maximal rational rankLocus of complete curves on $mathcal M_g$What is the expected dimension of the Zariski closure of the rational points on the moduli space of curves?Motivic fundamental group of the moduli space of curves?How to calculate tautological classes of some varieties?
$begingroup$
Let $X$ be a quasiprojective variety over $mathbf C$. Take the union of all projective subvarieties $W subseteq X$ that have dimension at least $1$. Is the result Zariski closed?
(I was wondering this in the particular setting $X = mathcal M_g$, where the projective subvarieties have been the subject of some study. But the general question seems natural as well.)
ag.algebraic-geometry
edited 9 hours ago
Mark
1,049714
asked 9 hours ago
user141570user141570
211
New contributor
user141570 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Let $X$ be a quasiprojective variety over $mathbf C$. Take the union of all projective subvarieties $W subseteq X$ that have dimension at least $1$. Is the result Zariski closed?
(I was wondering this in the particular setting $X = mathcal M_g$, where the projective subvarieties have been the subject of some study. But the general question seems natural as well.)
ag.algebraic-geometry
edited 9 hours ago
Mark
1,049714
asked 9 hours ago
user141570user141570
211
New contributor
user141570 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Let $X$ be a quasiprojective variety over $mathbf C$. Take the union of all projective subvarieties $W subseteq X$ that have dimension at least $1$. Is the result Zariski closed?
(I was wondering this in the particular setting $X = mathcal M_g$, where the projective subvarieties have been the subject of some study. But the general question seems natural as well.)
ag.algebraic-geometry
edited 9 hours ago
Mark
1,049714
asked 9 hours ago
user141570user141570
211
New contributor
user141570 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Let $X$ be a quasiprojective variety over $mathbf C$. Take the union of all projective subvarieties $W subseteq X$ that have dimension at least $1$. Is the result Zariski closed?
(I was wondering this in the particular setting $X = mathcal M_g$, where the projective subvarieties have been the subject of some study. But the general question seems natural as well.)
ag.algebraic-geometry
ag.algebraic-geometry
edited 9 hours ago
Mark
1,049714
asked 9 hours ago
user141570user141570
211
New contributor
user141570 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 9 hours ago
Mark
1,049714
asked 9 hours ago
user141570user141570
211
New contributor
user141570 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 9 hours ago
Mark
1,049714
edited 9 hours ago
Mark
1,049714
edited 9 hours ago
Mark
1,049714
1,049714
asked 9 hours ago
user141570user141570
211
New contributor
user141570 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 9 hours ago
user141570user141570
211
asked 9 hours ago
user141570user141570
211
211
New contributor
user141570 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user141570 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
No. For example take $X = mathbbA^1 times mathbbP^1$ minus one point, say $(x,y)$. Then $W = (mathbbA^1 setminus x) times mathbbP^1$ is not closed.
answered 8 hours ago
SashaSasha
21.8k22859
$endgroup$
$begingroup$
Oops, good point.
$endgroup$
– Mark
6 hours ago
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "504"
;
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
);
);
user141570 is a new contributor. Be nice, and check out our Code of Conduct.
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%2f333422%2fprojective-subvarieties-of-a-quasiprojective-variety%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
$begingroup$
No. For example take $X = mathbbA^1 times mathbbP^1$ minus one point, say $(x,y)$. Then $W = (mathbbA^1 setminus x) times mathbbP^1$ is not closed.
answered 8 hours ago
SashaSasha
21.8k22859
$endgroup$
$begingroup$
Oops, good point.
$endgroup$
– Mark
6 hours ago
add a comment |
$begingroup$
No. For example take $X = mathbbA^1 times mathbbP^1$ minus one point, say $(x,y)$. Then $W = (mathbbA^1 setminus x) times mathbbP^1$ is not closed.
answered 8 hours ago
SashaSasha
21.8k22859
$endgroup$
$begingroup$
Oops, good point.
$endgroup$
– Mark
6 hours ago
add a comment |
$begingroup$
No. For example take $X = mathbbA^1 times mathbbP^1$ minus one point, say $(x,y)$. Then $W = (mathbbA^1 setminus x) times mathbbP^1$ is not closed.
answered 8 hours ago
SashaSasha
21.8k22859
$endgroup$
No. For example take $X = mathbbA^1 times mathbbP^1$ minus one point, say $(x,y)$. Then $W = (mathbbA^1 setminus x) times mathbbP^1$ is not closed.
answered 8 hours ago
SashaSasha
21.8k22859
answered 8 hours ago
SashaSasha
21.8k22859
answered 8 hours ago
SashaSasha
21.8k22859
answered 8 hours ago
SashaSasha
21.8k22859
21.8k22859
$begingroup$
Oops, good point.
$endgroup$
– Mark
6 hours ago
add a comment |
$begingroup$
Oops, good point.
$endgroup$
– Mark
6 hours ago
$begingroup$
Oops, good point.
$endgroup$
– Mark
6 hours ago
$begingroup$
Oops, good point.
$endgroup$
– Mark
6 hours ago
add a comment |
user141570 is a new contributor. Be nice, and check out our Code of Conduct.
user141570 is a new contributor. Be nice, and check out our Code of Conduct.
user141570 is a new contributor. Be nice, and check out our Code of Conduct.
user141570 is a new contributor. Be nice, and check out our Code of Conduct.
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.
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%2f333422%2fprojective-subvarieties-of-a-quasiprojective-variety%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
