On the Topologies on ind-Varieties and related Irreducibility Questions
Algebraic Geometry
2016-11-24 v3
Abstract
In the literature there are two ways of endowing an affine ind-variety with a topology. One possibility is due to Shafarevich and the other to Kambayashi. In this paper we specify a large class of affine ind-varieties where these two topologies differ. We give an example of an affine ind-variety that is reducible with respect to Shafarevich's topology, but irreducible with respect to Kambayashi's topology. Moreover, we give a counter-example of a supposed irreducibility criterion of Shafarevich which is different from a counter-example given by Homma. We finish the paper with an irreducibility criterion similar to the one given by Shafarevich.
Keywords
Cite
@article{arxiv.1109.4088,
title = {On the Topologies on ind-Varieties and related Irreducibility Questions},
author = {Immanuel Stampfli},
journal= {arXiv preprint arXiv:1109.4088},
year = {2016}
}
Comments
11 pages, typos corrected, minor changes, improved exposition