On local accumulation complexity of the set of log canonical volumes in dimension $\geq 2$

TL;DR

This paper demonstrates that the set of log canonical volumes in dimensions two and higher can have an infinitely complex local accumulation structure, revealing new insights into their geometric properties.

Contribution

It establishes that the local accumulation complexity of log canonical volumes in dimension at least two can be infinite, a previously unknown phenomenon.

Findings

The set of log canonical volumes can have infinite local accumulation complexity.

This reveals new geometric complexity in higher-dimensional algebraic varieties.

The result impacts the understanding of volume behavior in algebraic geometry.

Abstract

We prove that the local accumulation complexity of the set of log canonical volumes in dimension $\geq 2$ can be infinite.