Local property of a flat family of schemes
$begingroup$
Let $pi: X to S$ be a flat, smooth family of genus $0$ curves, for example. Now take a point $x in S$, then $x in pi{-1}(p)$ from some $p in S$, i.e $x in mathbb{P}^1$.
I am trying to relate such families to first order infinitesimal deformations.
In particular, does there exist an open subset $ xin U subset X$ such that $U$ is a first order infinitesimal deformation of $mathbb{P}^1$?
algebraic-geometry commutative-algebra deformation-theory
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,02311024
$endgroup$
add a comment |
$begingroup$
Let $pi: X to S$ be a flat, smooth family of genus $0$ curves, for example. Now take a point $x in S$, then $x in pi{-1}(p)$ from some $p in S$, i.e $x in mathbb{P}^1$.
I am trying to relate such families to first order infinitesimal deformations.
In particular, does there exist an open subset $ xin U subset X$ such that $U$ is a first order infinitesimal deformation of $mathbb{P}^1$?
algebraic-geometry commutative-algebra deformation-theory
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,02311024
$endgroup$
$begingroup$
In your first paragraph, $x in S$ and (presumably) $x in pi^{-1}(p)$, which doesn't make sense.
$endgroup$
– RghtHndSd
Dec 12 '18 at 3:31
add a comment |
$begingroup$
Let $pi: X to S$ be a flat, smooth family of genus $0$ curves, for example. Now take a point $x in S$, then $x in pi{-1}(p)$ from some $p in S$, i.e $x in mathbb{P}^1$.
I am trying to relate such families to first order infinitesimal deformations.
In particular, does there exist an open subset $ xin U subset X$ such that $U$ is a first order infinitesimal deformation of $mathbb{P}^1$?
algebraic-geometry commutative-algebra deformation-theory
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,02311024
$endgroup$
Let $pi: X to S$ be a flat, smooth family of genus $0$ curves, for example. Now take a point $x in S$, then $x in pi{-1}(p)$ from some $p in S$, i.e $x in mathbb{P}^1$.
I am trying to relate such families to first order infinitesimal deformations.
In particular, does there exist an open subset $ xin U subset X$ such that $U$ is a first order infinitesimal deformation of $mathbb{P}^1$?
algebraic-geometry commutative-algebra deformation-theory
algebraic-geometry commutative-algebra deformation-theory
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,02311024
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,02311024
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,02311024
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,02311024
asked Dec 4 '18 at 20:01
JadwigaJadwiga
2,02311024
2,02311024
$begingroup$
In your first paragraph, $x in S$ and (presumably) $x in pi^{-1}(p)$, which doesn't make sense.
$endgroup$
– RghtHndSd
Dec 12 '18 at 3:31
add a comment |
$begingroup$
In your first paragraph, $x in S$ and (presumably) $x in pi^{-1}(p)$, which doesn't make sense.
$endgroup$
– RghtHndSd
Dec 12 '18 at 3:31
$begingroup$
In your first paragraph, $x in S$ and (presumably) $x in pi^{-1}(p)$, which doesn't make sense.
$endgroup$
– RghtHndSd
Dec 12 '18 at 3:31
$begingroup$
In your first paragraph, $x in S$ and (presumably) $x in pi^{-1}(p)$, which doesn't make sense.
$endgroup$
– RghtHndSd
Dec 12 '18 at 3:31
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
});
}
});
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%2f3026081%2flocal-property-of-a-flat-family-of-schemes%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%2f3026081%2flocal-property-of-a-flat-family-of-schemes%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
$begingroup$
In your first paragraph, $x in S$ and (presumably) $x in pi^{-1}(p)$, which doesn't make sense.
$endgroup$
– RghtHndSd
Dec 12 '18 at 3:31