Scheme-theoretic intersection
id:
scheme-theoretic-intersection-291-10278948
title:
Scheme-theoretic intersection
text:
In algebraic geometry, the scheme-theoretic intersection of closed subschemes X, Y of a scheme W is X × W Y , the fiber product of the closed immersions X ↪ W , Y ↪ W . It is denoted by X ∩ Y . Locally, W is given as Spec R for some ring R and X, Y as Spec , Spec for some ideals I, J. Thus, locally, the intersection X ∩ Y is given as Here, we used R / I ⊗ R R / J ≃ R / Example: Let X ⊂ P n be a projective variety with the homogeneous coordinate ring S/I, where S is a polynomial ring. If H
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wiki
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encyclopedia
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original url:
https://en.wikipedia.org/wiki/Scheme-theoretic_intersection
date created:
date modified:
2022-11-03T14:39:18Z
main entity:
{"identifier":"Q28456520","url":"https://www.wikidata.org/entity/Q28456520"}
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