The pre-Tango structure is an ample invertible sheaf of locally exact differentials on a variety of positive characteristic. It is well known that pre-Tango structures on curves often induce pathological uniruled surfaces. We show that almost all pre-Tango structures on varieties induce higher-dimensional pathological uniruled varieties, and that each of these uniruled varieties also has a pre-Tango structure. For this purpose, we first consider the p-closed rational vector field induced by a pre-Tango structure, and the smoothness of the fibration induced by the p-closed rational vector field. Moreover, we give two examples: of a 3-dimensional variety of general type whose automorphism group scheme is not reduced, and of a non-uniruled variety which has a pre-Tango structure inducing a higher-dimensional pathological uniruled variety.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-2-4,
author = {Yoshifumi Takeda},
title = {Pre-Tango structures and uniruled varieties},
journal = {Colloquium Mathematicae},
volume = {107},
year = {2007},
pages = {193-216},
zbl = {1108.14014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-2-4}
}
Yoshifumi Takeda. Pre-Tango structures and uniruled varieties. Colloquium Mathematicae, Tome 107 (2007) pp. 193-216. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-2-4/