Singularities of general fibers and the LMMP
Zsolt Patakfalvi, Joe Waldron
Abstract
We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to a divisor with positive integer coefficients divisible by p -1. We deduce many consequences about the fibrations of the minimal model program: for example the general fibers of terminal Mori fiber spaces of relative dimension 2 are normal in characteristic p 5 and smooth in characteristic p 11.
Topics & Concepts
MathematicsDivisor (algebraic geometry)Gravitational singularityInteger (computer science)Base (topology)FiberBase changeDimension (graph theory)Pure mathematicsDiscrete mathematicsMathematical analysisOrganic chemistryChemistryComputer scienceProgramming languageAlgebraic Geometry and Number TheoryAdvanced Differential Equations and Dynamical SystemsHomotopy and Cohomology in Algebraic Topology