On the Morrison-Kawamata dream space and its applications

TL;DR

This paper introduces the theory of Morrison-Kawamata dream spaces, providing a framework for varieties satisfying the cone conjecture, and applies it to deformation invariance and boundedness problems in algebraic geometry.

Contribution

It develops the theory of Morrison-Kawamata dream spaces and demonstrates their applications to deformation invariance and boundedness in algebraic geometry.

Findings

Established generic deformation invariance of cones

Applied theory to boundedness problems

Provided axiomatic framework for varieties satisfying the cone conjecture

Abstract

We develop the theory of Morrison-Kawamata dream spaces, which axiomatizes varieties (not necessarily of Calabi-Yau type) that satisfy the Morrison-Kawamata cone conjecture. Using this theory, we establish the generic deformation invariance of various cones and apply it to the boundedness problem of algebraic varieties.