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
Keywords:
DB singularities
,
deformation
,
Du Bois singularities
,
log canonical singularities
,
non-lc ideal
Rights: Copyright © 2016 Mathematical Society of Japan
