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**There is a page named "Zariski's connectedness theorem" on Wikipedia**

- geometry, Zariski's connectedness theorem (due to Oscar Zariski) says that under certain conditions the fibers of a morphism of varieties are connected. It...2 KB (203 words) - 19:02, 18 February 2023
- It is the special case of Zariski's connectedness theorem when the two varieties are birational. Zariski's main theorem can be stated in several ways...11 KB (1,601 words) - 10:54, 25 June 2024
- f} the natural inclusion. Zariski's connectedness theorem Grothendieck's connectedness theorem Deligne's connectedness theorem Fulton, William; Hansen,...2 KB (293 words) - 09:55, 9 October 2024
- connectedness theorem Hartshorne's connectedness theorem Zariski's connectedness theorem, a generalization of Zariski's main theorem This disambiguation page lists...322 bytes (63 words) - 13:46, 21 September 2016
- less than k is connected. It is a local analogue of Bertini's theorem. Zariski connectedness theorem Fulton–Hansen connectedness theorem Grothendieck &...2 KB (160 words) - 23:37, 26 December 2023
- But, by Zariski's connectedness theorem, the last part in the above says that the fiber f ′ − 1 ( s ) {\displaystyle f'^{-1}(s)} is connected for any...2 KB (425 words) - 04:31, 23 October 2024
- {O}}_{Y}} or, equivalently, the geometric fibers are all connected (Zariski's connectedness theorem). It is also commonly called an algebraic fiber space...2 KB (295 words) - 18:57, 13 May 2022
- Zahorski theorem (real analysis) Zariski's connectedness theorem (algebraic geometry) Zariski's main theorem (algebraic geometry) Zeckendorf's theorem (number...73 KB (6,030 words) - 15:22, 20 October 2024
- Max Noether theorem on canonical curves)geometrically integral and all fibers are geometrically connected (by Zariski's connectedness theorem). In particular, for a fiber F = ∑ i = 1 n a i E i {\displaystyle...16 KB (2,529 words) - 11:12, 9 October 2024

In mathematics, the Borel–Weil–Bott theorem is a basic result in the representation theory of Lie groups, showing how a family of representations can...

13 KB (1,903 words) - 10:40, 23 July 2024

Lueroth's theorem)

rationally connected if every two points are connected by a rational curve contained in the variety. This definition differs from that of path connectedness only...

12 KB (1,547 words) - 10:12, 20 July 2024

Unitarian trick (section Weyl's theorem)

compact groups, or connected semisimple Lie groups and complex semisimple Lie algebras goes sometimes under the name of Weyl's theorem. A related result...

7 KB (974 words) - 20:16, 29 July 2024

passage to limit. The theorem is used to deduce some other important theorems: Stein factorization and a version of Zariski's main theorem that says that a...

4 KB (916 words) - 13:53, 29 July 2022

Rapinchuk (1994), Theorem 3.1. Borel (1991), Theorem 20.9(i). Steinberg (2016), Theorem 8. Steinberg (2016), Theorem 30. Tits (1964), Main Theorem; Gille (2009)...

55 KB (7,845 words) - 18:28, 24 April 2024

List of general topology topics (section Connectedness)

Sperner's lemma Simplicial approximation theorem Nerve of an open covering Simply connected Semi-locally simply connected Path (topology) Homotopy Homotopy lifting...

5 KB (393 words) - 12:17, 30 October 2023

Poincaré lemma (section Simply connected case)

can be computed as the de Rham cohomology of it, that is, the de Rham theorem, relies on the Poincaré lemma. It does, however, mean that it is enough...

25 KB (4,404 words) - 08:14, 24 September 2024

- irreducible spaces. Theorem 21.3: Every irreducible space X {\displaystyle X} is connected and locally connected. Proof: 1. Connectedness: Assume X = U ∪