If C and D are irreducible, affine varieties over an algebraically closed field, and I form the product variety CxD, is the projection morphism from CxD to C necessarily an open map? That is, is the projection of each Zariski open subset of CxD necessarily Zariski open in C?
Take the 2minute tour
×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Yes. More generally, flat morphisms locally of finite presentation are universally open (EGA IV_{2}, Théorème 2.4.6). 

