Base change behavior of the relative canonical sheaf related to higher dimensional moduli
Algebraic Geometry
2013-06-25 v3
Abstract
We show that the compatibility of the relative canonical sheaf with base change fails generally in families of normal varieties. Furthermore, it always fails if the general fiber of a family of pure dimension n is Cohen-Macaulay and the special fiber contains a strictly S_{n-1} point. In particular, in moduli spaces with functorial relative canonical sheaves Cohen-Macaulay schemes can not degenerate to S_{n-1} schemes. Another, less immediate consequence is that the canonical sheaf of an S_{n-1}, G_2 scheme of pure dimension n is not S_3.
Keywords
Cite
@article{arxiv.1005.5207,
title = {Base change behavior of the relative canonical sheaf related to higher dimensional moduli},
author = {Zsolt Patakfalvi},
journal= {arXiv preprint arXiv:1005.5207},
year = {2013}
}
Comments
Third, updated version. Minor changes, the non-standard usage of S_d at a point replaced by the adequate depth conditions. Comments are welcome