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On the relative cone conjecture for families of IHS manifolds

Andreas Höring, Gianluca Pacienza, Zhixin Xie

Abstract

We study the relative cone conjecture for families of $K$-trivial varieties with vanishing irregularity. As an application we prove that the relative movable and the relative nef cone conjectures hold for fibrations in projective IHS manifolds of the 4 known deformation types.

On the relative cone conjecture for families of IHS manifolds

Abstract

We study the relative cone conjecture for families of -trivial varieties with vanishing irregularity. As an application we prove that the relative movable and the relative nef cone conjectures hold for fibrations in projective IHS manifolds of the 4 known deformation types.

Paper Structure

This paper contains 12 sections, 124 equations.

Table of Contents

  1. Introduction
  2. Notation and basic definitions
  3. The relative setting
  4. Rational maps
  5. Cones and cone conjectures
  6. Birational geometry
  7. The geography of models for Klt fibrations
  8. On the relative movable and nef cone conjectures
  9. Fibrations in IHS manifolds
  10. A family of K3 surfaces
  11. The relative automorphism group
  12. An interesting SQM

Theorems & Definitions (25)

  • proof : Proof of Lemma \ref{['lem:rel_to_abs']}
  • proof
  • proof : Proof of Lemma \ref{['lemma-regular']}
  • proof
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  • proof
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  • ...and 15 more