Talk:Smooth morphism

This is not yet defined in the glossary!--129.70.14.128 (talk) 01:26, 20 November 2007 (UTC)

"Geometric point"
The definition of "geometric point" appearing in the glossary requires that the scheme in question be defined over a field. What is the appropriate definition in the general case? 98.243.172.55 (talk) 19:23, 7 December 2013 (UTC)


 * A geometric point of X is $$\operatorname{Spec}(k) \to X$$ where k is a separably closed field. -- Taku (talk) 14:17, 17 December 2013 (UTC)

Examples Needed
This page should discuss examples of smooth morphisms


 * trivial fibrations
 * Hirzebruch surfaces over $$\mathbb{P}^1$$
 * scrolls
 * vector bundles
 * smooth locus of flat families
 * etale morphisms

and non-examples, such as
 * families of singular varieties
 * singular variety over a point
 * blowups — Preceding unsigned comment added by 97.122.75.155 (talk) 17:31, 1 August 2017 (UTC)

Smooth Locus of Families
This page should discuss how to find the smooth locus of a morphism of schemes $$X \to S$$. — Preceding unsigned comment added by 97.122.75.155 (talk) 05:12, 4 August 2017 (UTC)


 * I believe this is a version of Bertini's theorem (no question it's an important thing to cover). -- Taku (talk) 23:20, 8 August 2017 (UTC)