Vol. 10, No. 5, 2016

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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

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 X0 with Du Bois singularities and the general fiber has rational singularities, then the total space has rational singularities near X0.

Du Bois singularities, rational singularities, inversion of adjunction, vanishing theorems
Mathematical Subject Classification 2010
Primary: 14J17
Secondary: 14E99, 14J10, 14D06, 14B05
Received: 23 January 2015
Revised: 17 March 2016
Accepted: 27 April 2016
Published: 28 July 2016
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