The α-invariant and Thompson's conjecture

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2 Scopus citations


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 languageEnglish (US)
Article numbere5
JournalForum of Mathematics, Pi
StatePublished - Jan 1 2016

ASJC Scopus subject areas

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

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