The α-invariant and Thompson's conjecture

Pham Huu Tiep

doi:10.1017/fmp.2016.3

The α-invariant and Thompson's conjecture

Pham Huu Tiep

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In 1981, Thompson proved that, if is any integer and is any finite subgroup of, then has a semi-invariant of degree at most. He conjectured that, in fact, there is a universal constant such that for any and any finite subgroup <![CDATA[G, has a semi-invariant of degree at most. This conjecture would imply that the-invariant, as introduced by Tian in 1987, is at most. We prove Thompson's conjecture in this paper.

Original language	English (US)
Article number	e5
Journal	Forum of Mathematics, Pi
Volume	4
DOIs	https://doi.org/10.1017/fmp.2016.3
State	Published - 2016

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1017/fmp.2016.3

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abstract = "In 1981, Thompson proved that, if is any integer and is any finite subgroup of, then has a semi-invariant of degree at most. He conjectured that, in fact, there is a universal constant such that for any and any finite subgroup <![CDATA[G, has a semi-invariant of degree at most. This conjecture would imply that the-invariant, as introduced by Tian in 1987, is at most. We prove Thompson's conjecture in this paper.",

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AB - In 1981, Thompson proved that, if is any integer and is any finite subgroup of, then has a semi-invariant of degree at most. He conjectured that, in fact, there is a universal constant such that for any and any finite subgroup <![CDATA[G, has a semi-invariant of degree at most. This conjecture would imply that the-invariant, as introduced by Tian in 1987, is at most. We prove Thompson's conjecture in this paper.

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The α-invariant and Thompson's conjecture

Abstract

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