Accumulation point theorem for generalized log canonical thresholds

TL;DR

This paper proves that the accumulation points of generalized log canonical thresholds in higher dimensions are derived from those in one lower dimension, revealing a dimensional hierarchy in their structure.

Contribution

It establishes a new connection between accumulation points of generalized log canonical thresholds across dimensions, advancing understanding of their behavior in algebraic geometry.

Findings

Accumulation points in dimension n relate to thresholds in dimension n-1.

The set of accumulation points is characterized by thresholds in lower dimensions.

Provides a recursive structure for analyzing generalized log canonical thresholds.

Abstract

In this paper we show that the set of accumulation points of generalized log canonical thresholds for certain DCC sets comes from the set of generalized log canonical thresholds of dimension $1$ less of the same DCC sets.