ag.algebraic geometry - Does a birational involution of C^n always have
a fixed point?
The answer is no. There are plenty of counterexamples, for example the map given by "a-fortiori", which is (x,y)mapsto(x+1/y,−y), which can be generalised to any dimension.
The good question is probably to look at birational involutions of mathbbPn.
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