We give an example of a representation of the Kronecker quiver for which the closure of the corresponding orbit contains a singularity smoothly equivalent to the isolated singularity of two planes crossing at a point. Therefore this orbit closure is neither Cohen-Macaulay nor unibranch.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-1-8,
author = {Grzegorz Zwara},
title = {An orbit closure for a representation of the Kronecker quiver with bad singularities},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {81-86},
zbl = {1054.14004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-1-8}
}
Grzegorz Zwara. An orbit closure for a representation of the Kronecker quiver with bad singularities. Colloquium Mathematicae, Tome 96 (2003) pp. 81-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-1-8/