Assume that X,Y are integral noetherian affine schemes. Let f:X → Y be a dominant, generically finite morphism of finite type. We show that the set of points at which the morphism f is not finite is either empty or a hypersurface. An example is given to show that this is no longer true in the non-noetherian case.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm92-1-5,
author = {Zbigniew Jelonek and Marek Kara\'s},
title = {The set of points at which a morphism of affine schemes is not finite},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {59-66},
zbl = {0996.14030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm92-1-5}
}
Zbigniew Jelonek; Marek Karaś. The set of points at which a morphism of affine schemes is not finite. Colloquium Mathematicae, Tome 91 (2002) pp. 59-66. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm92-1-5/