### 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) |
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Article number | e5 |

Journal | Forum of Mathematics, Pi |

Volume | 4 |

DOIs | |

Publication status | Published - Jan 1 2016 |

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### ASJC Scopus subject areas

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