Translator Disclaimer
VOL. 70 | 2016 Du Bois singularities deform
Sándor J. Kovács, Karl Schwede

Editor(s) János Kollár, Osamu Fujino, Shigeru Mukai, Noboru Nakayama

Abstract

Let $X$ be a variety and $H$ a Cartier divisor on $X$. We prove that if $H$ has Du Bois (or DB) singularities, then $X$ has Du Bois singularities near $H$. As a consequence, if $X \to S$ is a proper flat family over a smooth curve $S$ whose special fiber has Du Bois singularities, then the nearby fibers also have Du Bois singularities. We prove this by obtaining an injectivity theorem for certain maps of canonical modules. As a consequence, we also obtain a restriction theorem for certain non-lc ideals.

Information

Published: 1 January 2016
First available in Project Euclid: 4 October 2018

zbMATH: 1369.14009
MathSciNet: MR3617778

Digital Object Identifier: 10.2969/aspm/07010049

Subjects:
Primary: 14B05, 14B07, 14F17, 14F18

Rights: Copyright © 2016 Mathematical Society of Japan

PROCEEDINGS ARTICLE
17 PAGES


SHARE
Back to Top