Open Access
Translator Disclaimer
2013 Base change behavior of the relative canonical sheaf related to higher dimensional moduli
Zsolt Patakfalvi
Algebra Number Theory 7(2): 353-378 (2013). DOI: 10.2140/ant.2013.7.353

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 Sn1 point. In particular, in moduli spaces with functorial relative canonical sheaves Cohen–Macaulay schemes can not degenerate to Sn1 schemes. Another, less immediate consequence is that the canonical sheaf of an Sn1, G2 scheme of pure dimension n is not S3.

Citation

Download Citation

Zsolt Patakfalvi. "Base change behavior of the relative canonical sheaf related to higher dimensional moduli." Algebra Number Theory 7 (2) 353 - 378, 2013. https://doi.org/10.2140/ant.2013.7.353

Information

Received: 9 June 2011; Revised: 26 January 2012; Accepted: 9 March 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1273.14073
MathSciNet: MR3123642
Digital Object Identifier: 10.2140/ant.2013.7.353

Subjects:
Primary: 14J10
Secondary: 14D06, 14E30, 14F10

Rights: Copyright © 2013 Mathematical Sciences Publishers

JOURNAL ARTICLE
26 PAGES


SHARE
Vol.7 • No. 2 • 2013
MSP
Back to Top