m at h . A G ] 1 0 M ay 1 99 9 FIXED POINTS OF GROUP ACTIONS AND RATIONAL MAPS
نویسنده
چکیده
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-equivariant rational map E 99K Y . By induction, there is a fixed point on Y .
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