Rational fixed points for linear group actions
نویسندگان
چکیده
منابع مشابه
Rational Fixed Points for Linear Group Actions
Pietro Corvaja §1 Introduction. A general principle in the theory of diophantine equations asserts that if an equation admits " many " rational solutions, there should be a geometric reason explaining such abundance. We consider here a (multiplicative) semigroup of N ×N matrices with rational entries: we suppose that all of them admit rational eigenvalues and deduce the natural geometrical cons...
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Proof. The proof is by induction on dimX. The case dimX = 0 is clear. Let x ∈ X be a smooth H-fixed point and consider the blow up BxX with exceptional divisor E ∼= P. The H-action lifts to BxX and so we get an H-action on E which has a fixed point by (1.1). Since Y is proper, the induced rational map BxX → X 99K Y is defined outside a subset of codimension at least 2. Thus we get an H-equivari...
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ژورنال
عنوان ژورنال: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
سال: 2009
ISSN: 2036-2145,0391-173X
DOI: 10.2422/2036-2145.2007.4.04