Fulton–Hansen connectedness theorem
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. It is named after William Fulton and Johan Hansen, who proved it in 1979.
More generally, the theorem states that if is a projective variety and is any morphism such that , then is connected, where is the diagonal in . The special case of intersections is recovered by taking , with the natural inclusion.
- Fulton, William; Hansen, Johan (1979). "A connectedness theorem for projective varieties with applications to intersections and singularities of mappings". Annals of Mathematics. 110 (1): 159–166. doi:10.2307/1971249. JSTOR 1971249.
- Lazarsfeld, Robert (2004). Positivity in algebraic geometry, Vol. I. Berlin: Springer. ISBN 3-540-22533-1. Positivity in algebraic geometry, Vol. II. 2004. ISBN 3-540-22534-X.