Variation of Stable Birational Types of Hypersurfaces
Algebraic Geometry
2019-10-10 v3
Abstract
We introduce and study the question how can stable birational types vary in a smooth proper family. Our starting point is the specialization for stable birational types of Nicaise and the author and our emphasis is on stable birational types of hypersurfaces. Building up on the work of Totaro and Schreieder on stable irrationality of hypersurfaces of high degree, we show that smooth Fano hypersurfaces of large degree over a field of characteristic zero are in general not stably birational to each other. In the appendix Claire Voisin proves a similar result in a different setting using the Chow decomposition of diagonal and unramified cohomology.
Keywords
Cite
@article{arxiv.1903.02111,
title = {Variation of Stable Birational Types of Hypersurfaces},
author = {Evgeny Shinder and with an appendix by Claire Voisin},
journal= {arXiv preprint arXiv:1903.02111},
year = {2019}
}
Comments
Slightly improved exposition; added reference to work of Schreieder on generalization to char. p