Notes on Kodaira energies of polarized varieties

TL;DR

This paper explores the properties of Kodaira energies in polarized varieties, proposing conjectures and presenting partial results, especially focusing on three-dimensional cases, to deepen understanding of their geometric significance.

Contribution

It introduces new conjectures related to Kodaira energies and provides partial results, advancing the theoretical understanding of polarized varieties in algebraic geometry.

Findings

Proposed conjectures on Kodaira energies.

Partial results for three-dimensional cases.

Insights into the behavior of Kodaira energies in polarized varieties.

Abstract

The Kodaira energy of a polarized manifold (M,L) is defined by \kappa\epsilon(M,L)=-Inf{t\in Q|\kappa(K+tL)\ge 0}. Here we propose a couple of conjectures and announce several partial results. 3-dimensional cases are mainly considered. A hard copy is available on request to the author.