F-singularities in families

Karl Schwede; Wenliang Zhang; Zsolt Patakfalvi

F-singularities in families

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arxiv 1305.1646 v3 pith:FMEGI7PR submitted 2013-05-07 math.AG math.AC

Zsolt Patakfalvi , Karl Schwede , Wenliang Zhang This is my paper · ORCID

classification math.AGmath.AC

keywords familiesidealsadjointbehaviorbundlescertainf-singularitiesline

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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.

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On the canonical bundle formula and effective birationality for Fano varieties in char $p>0$
math.AG 2025-01 conditional novelty 6.0 of 10

The paper establishes a canonical bundle formula for Fano-type threefold fibrations in large characteristic and proves effective birationality for strongly F-regular weak Fano varieties with bounded Gorenstein index.

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