Valuative independence and metric SYZ conjecture

TL;DR

This paper proves the metric SYZ conjecture for polarized maximal degenerations of Calabi-Yau manifolds under a valuative independence condition on the section ring.

Contribution

It establishes the metric SYZ conjecture assuming the existence of a canonical basis satisfying valuative independence.

Findings

Proves the metric SYZ conjecture under specific algebraic conditions.

Introduces the valuative independence condition as key to the proof.

Connects algebraic properties of the section ring to geometric conjectures.

Abstract

Given a polarised maximal degeneration of compact Calabi-Yau manifolds, assuming there exists a canonical basis of the section ring for the polarisation line bundle, satisfying the valuative independence condition, we will prove the metric SYZ conjecture.