Infinite geodesic rays in the space of Kahler potentials

TL;DR

This paper establishes a geometric link between algebraic degenerations and geodesic rays in the space of Kähler potentials, providing a new method to construct infinite-length geodesics from degenerations.

Contribution

It introduces a novel geometric construction that associates special algebraic degenerations with infinite geodesic rays in the space of Kähler potentials.

Findings

Constructs infinite geodesic rays from algebraic degenerations.

Provides a general geometric framework for geodesic solutions.

Links algebraic degenerations to geometric properties of Kähler metrics.

Abstract

In this paper we explore the connection between special degenerations of algebraic manifolds and geodesics in the space of Kahler metrics. We provide a new and general geometric construction of nontrivial solutions for the geodesic equation. We show how to associate to any special nontrivial degeneration a geodesic of inifite length.