F-singularities in families

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.

60 pages, typos corrected throughout and improved exposition, to appear in Algebraic Geometry

References in corpus (6)

• Depth of $F$-singularities and base change of relative canonical sheaves
• On the three dimensional minimal model program in positive characteristic
• The trace map of Frobenius and extending sections for threefolds
• Semi-positivity in positive characteristics
• On the numerical dimension of pseudo-effective divisors in positive characteristic
• Pluri-canonical maps of varieties of maximal Albanese dimension in positive characteristic

Cited by in corpus (6)

• Nef anti-canonical divisors and rationally connected fibrations
• Abundance for non-uniruled 3-folds with non-trivial Albanese maps in positive characteristics
• Semiample perturbations for log canonical varieties over an F-finite field containing an infinite perfect field
• A note on Iitaka's conjecture $C_{3,1}$ in positive characteristics
• Weak positivity theorem and Frobenius stable canonical rings of geometric generic fibers
• On Rational Connectedness of Globally F-Regular Threefolds