Inversion of adjunction for rational and Du Bois pairs

Kovács, Sándor; Schwede, Karl

doi:10.2140/ant.2016.10.969

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Inversion of adjunction for rational and Du Bois pairs

Sándor J. Kovács and Karl Schwede

Vol. 10 (2016), No. 5, 969–1000

DOI: 10.2140/ant.2016.10.969

Abstract

We prove several results about the behavior of Du Bois singularities and Du Bois pairs in families. Some of these generalize existing statements about Du Bois singularities to the pair setting while others are new even in the nonpair setting. We also prove a new inversion of adjunction result for Du Bois and rational pairs. In the nonpair setting this asserts that if a family over a smooth base has a special fiber $X_{0}$ with Du Bois singularities and the general fiber has rational singularities, then the total space has rational singularities near $X_{0}$ .

Keywords

Du Bois singularities, rational singularities, inversion of adjunction, vanishing theorems

Mathematical Subject Classification 2010

Primary: 14J17

Secondary: 14E99, 14J10, 14D06, 14B05

Milestones

Received: 23 January 2015

Revised: 17 March 2016

Accepted: 27 April 2016

Published: 28 July 2016

Authors

Sándor J. Kovács
Department of Mathematics University of Washington Box 354350 Padelford C-138 Seattle, WA 98195 United States

Karl Schwede
Department of Mathematics The University of Utah 155 S 1400 E Room 233 Salt Lake City, UT 84112-0090 United States

Vol. 10, No. 5, 2016