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Singularities of Generic Linkage of Algebraic Varieties
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 136, Number 6, December 2014
- pp. 1665-1691
- 10.1353/ajm.2014.0040
- Article
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Let $Y$ be a generic link of a subvariety $X$ of a nonsingular variety $A$. We give a description of
the Grauert-Riemenschneider canonical sheaf of $Y$ in terms of the multiplier ideal sheaves associated
to $X$ and use it to study the singularities of $Y$. As the first application, we give a criterion when
$Y$ has rational singularities and show that log canonical threshold increases and log canonical pairs
are preserved in generic linkage. As another application we give a quick and simple liaison method to
generalize the results of de Fernex-Ein and Chardin-Ulrich on the Castelnuovo-Mumford regularity bound
for a projective variety.