On del Pezzo fibrations in positive characteristic

Abstract

We establish two results on three-dimensional del Pezzo fibrations in positive characteristic. First, we give an explicit bound for torsion index of relatively torsion line bundles. Second, we show the existence of purely inseparable sections with explicit bounded degree. To prove these results, we study log del Pezzo surfaces defined over imperfect fields.

50 pages, v2: minor revisions, v3: minor revisions

References in corpus (2)

• Integral closure of ideals
• Invariants of algebraic varieties over imperfect fields

Cited by in corpus (11)

• Structure of geometrically non-reduced varieties
• Vanishing theorems for threefolds in characteristic $p>5$
• Invariants of algebraic varieties over imperfect fields
• On Kawamata--Viehweg type vanishing for three dimensional Mori fiber spaces in positive characteristic
• Vanishing theorems and adjoint linear systems on normal surfaces in positive characteristic
• Boundedness of regular del Pezzo surfaces over imperfect fields
• Bounding geometrically integral del Pezzo surfaces
• On p-power freeness in positive characteristic
• Rational points on 3-folds with nef anti-canonical class over finite fields
• Fibrations by plane quartic curves with a canonical moving singularity
• On singularity types of del Pezzo surfaces with rational double points in positive characteristic