|
|
| Line 1: |
Line 1: |
| In [[mathematics]], the '''Fulton–Hansen connectedness theorem''' is a result from [[intersection theory]] in [[algebraic geometry]], for the case of [[subvarieties]] of [[projective space]] with [[codimension]] large enough to make the intersection have components of dimension at least 1.
| | The person who wrote the post is called Jayson Hirano and he totally digs that name. Distributing production is how he makes a living. Ohio is where my home is but my husband wants us to transfer. To climb is something I truly enjoy performing.<br><br>Here is my webpage: clairvoyants - [http://www.january-yjm.com/xe/index.php?mid=video&document_srl=158289 go now] - |
| | |
| The formal statement is that if ''V'' and ''W'' are irreducible algebraic subvarieties of a [[projective space]] ''P'', all over an [[algebraically closed field]], and if
| |
| | |
| : dim(''V'') + dim (''W'') > dim (''P'')
| |
| | |
| in terms of the [[dimension of an algebraic variety]], then the intersection ''U'' of ''V'' and ''W'' is [[connected space|connected]].
| |
| | |
| More generally, the theorem states that if <math>Z</math> is a projective variety and <math>f:Z \to P^n \times P^n</math> is any morphism such that <math>\dim f(Z) > n</math>, then <math>f^{-1}\Delta</math> is connected, where <math>\Delta</math> is the [[diagonal]] in <math>P^n \times P^n</math>. The special case of intersections is recovered by taking <math>Z = V \times W</math>, with <math>f</math> the natural inclusion.
| |
| | |
| ==See also==
| |
| * [[Zariski's connectedness theorem]]
| |
| * [[Grothendieck's connectedness theorem]]
| |
| * [[Deligne's connectedness theorem]]
| |
| | |
| ==References==
| |
| * {{citation|first=W.|last= Fulton|first2= J. |last2=Hansen|title=A connectedness theorem for projective varieties with applications to intersections and singularities of mappings|journal= Annals of Math. |volume=110 |year=1979|pages= 159–166|doi=10.2307/1971249|jstor=1971249|issue=1|publisher=Annals of Mathematics}}
| |
| * {{citation|first=R.|last= Lazarsfeld|title=Positivity in Algebraic Geometry|publisher= Springer|year= 2004}}
| |
| | |
| ==External links==
| |
| * [http://www.math.unizh.ch/fileadmin/math/preprints/20-05.pdf PDF lectures withe the result as Theorem 15.3 (attributed to Faltings, also)]
| |
| | |
| {{DEFAULTSORT:Fulton-Hansen connectedness theorem}}
| |
| [[Category:Intersection theory]]
| |
| [[Category:Theorems in algebraic geometry]]
| |
The person who wrote the post is called Jayson Hirano and he totally digs that name. Distributing production is how he makes a living. Ohio is where my home is but my husband wants us to transfer. To climb is something I truly enjoy performing.
Here is my webpage: clairvoyants - go now -