F-singularities in families

2013/05/07 by Patakfalvi, Zsolt, Schwede, Karl, Zhang, Wenliang · 1 citation
#13A35 #13B40 #14B05 #14D05 #14F18 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1305.1646

Abstract

We study the behavior of test ideals and F-singularities in families. In particular, we obtain generic (and non-generic) restriction theorems for test ideals and non-F-pure ideals. Additionally, we study the global behavior of certain canonical linear systems (induced by Frobenius) associated to adjoint line bundles, in families. As a consequence, we obtain some positivity results for pushforwards of some adjoint line bundles and for certain subsheaves of these.

Cited by

• Bertini's theorem for F-rational F-pure singularities

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