Intersection Theory in the projective space
$begingroup$
Let $X$ be an irreducible projective variety embedded in $mathbb{P}^N$. Let $V,Wsubseteq X$ be two irreducible subprojective varieties intersecting properly in $X$, that is $$mathsf{codim}_X(V)+mathsf{codim}_X(W)=mathsf{codim}_X(Vcap W).$$ If we suppose $X$ smooth, then we can define by mean of the $mathsf{Tor}$-formula, the intersection product of $Vcdot_XW$. My question is the following:
Question: Can we find irreducible projective subvarieties $A,Bsubseteq mathbb{P}^N$ intersecting properly and such that $$Acdot_{mathbb{P}^N}B=Vcdot_XW $$?
Any help is well accepted.
intersection-theory
asked Jan 18 at 22:43
Vincenzo ZaccaroVincenzo Zaccaro
1,244720
$endgroup$
add a comment |
$begingroup$
Let $X$ be an irreducible projective variety embedded in $mathbb{P}^N$. Let $V,Wsubseteq X$ be two irreducible subprojective varieties intersecting properly in $X$, that is $$mathsf{codim}_X(V)+mathsf{codim}_X(W)=mathsf{codim}_X(Vcap W).$$ If we suppose $X$ smooth, then we can define by mean of the $mathsf{Tor}$-formula, the intersection product of $Vcdot_XW$. My question is the following:
Question: Can we find irreducible projective subvarieties $A,Bsubseteq mathbb{P}^N$ intersecting properly and such that $$Acdot_{mathbb{P}^N}B=Vcdot_XW $$?
Any help is well accepted.
intersection-theory
asked Jan 18 at 22:43
Vincenzo ZaccaroVincenzo Zaccaro
1,244720
$endgroup$
add a comment |
$begingroup$
Let $X$ be an irreducible projective variety embedded in $mathbb{P}^N$. Let $V,Wsubseteq X$ be two irreducible subprojective varieties intersecting properly in $X$, that is $$mathsf{codim}_X(V)+mathsf{codim}_X(W)=mathsf{codim}_X(Vcap W).$$ If we suppose $X$ smooth, then we can define by mean of the $mathsf{Tor}$-formula, the intersection product of $Vcdot_XW$. My question is the following:
Question: Can we find irreducible projective subvarieties $A,Bsubseteq mathbb{P}^N$ intersecting properly and such that $$Acdot_{mathbb{P}^N}B=Vcdot_XW $$?
Any help is well accepted.
intersection-theory
asked Jan 18 at 22:43
Vincenzo ZaccaroVincenzo Zaccaro
1,244720
$endgroup$
Let $X$ be an irreducible projective variety embedded in $mathbb{P}^N$. Let $V,Wsubseteq X$ be two irreducible subprojective varieties intersecting properly in $X$, that is $$mathsf{codim}_X(V)+mathsf{codim}_X(W)=mathsf{codim}_X(Vcap W).$$ If we suppose $X$ smooth, then we can define by mean of the $mathsf{Tor}$-formula, the intersection product of $Vcdot_XW$. My question is the following:
Question: Can we find irreducible projective subvarieties $A,Bsubseteq mathbb{P}^N$ intersecting properly and such that $$Acdot_{mathbb{P}^N}B=Vcdot_XW $$?
Any help is well accepted.
intersection-theory
intersection-theory
asked Jan 18 at 22:43
Vincenzo ZaccaroVincenzo Zaccaro
1,244720
asked Jan 18 at 22:43
Vincenzo ZaccaroVincenzo Zaccaro
1,244720
asked Jan 18 at 22:43
Vincenzo ZaccaroVincenzo Zaccaro
1,244720
asked Jan 18 at 22:43
Vincenzo ZaccaroVincenzo Zaccaro
1,244720
asked Jan 18 at 22:43
Vincenzo ZaccaroVincenzo Zaccaro
1,244720
1,244720
add a comment |
add a comment |
0
active
oldest
votes
Your Answer
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%2f3078838%2fintersection-theory-in-the-projective-space%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%2f3078838%2fintersection-theory-in-the-projective-space%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
