On threefold canonical thresholds

TL;DR

This paper proves that the set of threefold canonical thresholds obeys the ascending chain condition and characterizes those in the interval (1/2, 1), revealing a specific discrete set plus one value.

Contribution

It establishes the ascending chain condition for threefold canonical thresholds and explicitly describes the thresholds in a key interval, advancing understanding in algebraic geometry.

Findings

Set of threefold canonical thresholds satisfies ascending chain condition

Thresholds in (1/2, 1) are exactly {1/2 + 1/n} for n ≥ 3 and 4/5

Provides a precise description of thresholds in a specific interval

Abstract

We show that the set of threefold canonical thresholds satisfies the ascending chain condition. Moreover, we derive that threefold canonical thresholds in the interval $ (\frac{1}{2}, 1)$ consists of $ \{ \frac{1}{2}+\frac{1}{n}\}_{n \ge 3} \cup \{ \frac{4}{5}\}$.