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On the boundedness of $n$-folds with $κ(X)=n-1$

Stefano Filipazzi

Abstract

In this note we study certain sufficient conditions for a set of minimal klt pairs $(X,Δ)$ with $κ(X,Δ)=\dim(X)-1$ to be bounded.

On the boundedness of $n$-folds with $κ(X)=n-1$

Abstract

In this note we study certain sufficient conditions for a set of minimal klt pairs with to be bounded.

Paper Structure

This paper contains 18 sections, 19 theorems, 24 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Conventions
  4. Contractions
  5. Hyperstandard sets
  6. Divisors
  7. Pairs
  8. B-divisors
  9. Generalized pairs
  10. Canonical bundle formula
  11. Boundedness
  12. The geometric Tate--Shafarevich group
  13. Technical statements
  14. Examples
  15. Good minimal models
  16. ...and 3 more sections

Key Result

Theorem \oldthetheorem

Fix positive integers $n$ and $d$, a positive real number $v$, and a finite set of rational numbers $\mathcal{R} \subset \mathbb{Q} \cap [0,1]$. Let $\mathfrak{D}(n,v,\Phi(\mathcal{R}),d)$ be the set of minimal projective klt pairs $(X,\Delta)$ of dimension $n$ with $\kappa(X,\Delta)=n-1$, $\operato

Theorems & Definitions (60)

  • Theorem \oldthetheorem
  • Remark \oldthetheorem
  • Remark \oldthetheorem
  • Remark \oldthetheorem
  • Theorem \oldthetheorem
  • Example \oldthetheorem
  • Theorem \oldthetheorem
  • Remark \oldthetheorem
  • Remark \oldthetheorem
  • Definition \oldthetheorem
  • ...and 50 more