The Α-invariant and Thompson’s Conjecture
نویسنده
چکیده
In 1981, Thompson proved that, if n > 1 is any integer and G is any finite subgroup of GLn(C), then G has a semi-invariant of degree at most 4n2. He conjectured that, in fact, there is a universal constant C such that for any n ∈ N and any finite subgroup G < GLn(C), G has a semi-invariant of degree at most Cn. This conjecture would imply that the α-invariant αG(P), as introduced by Tian in 1987, is at most C . We prove Thompson’s conjecture in this paper. 2010 Mathematics Subject Classification: 20C15 (primary); 13A50, 14B05, 20C33 (secondary)
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تاریخ انتشار 2016