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On the algebraic and holomorphic social choice problem. (English) Zbl 1068.14040

Summary: Let \(X\) be an integral projective curve, \(n\geq 2\), and \(\delta_{X,n}: X\to X^n\) the diagonal map. Here we show the non-existence of morphisms \(\pi: X^n\to X\) such that \(\pi\circ h=\pi\) for every \(h\in S_n\) and \(\pi\circ\delta_{X,n}= \text{Id}_X\). We extend this non-existence result to non-everywhere defined maps. This is connected to the so-called social choice functions.

MSC:

14H99 Curves in algebraic geometry
14A15 Schemes and morphisms
32J18 Compact complex \(n\)-folds
91B14 Social choice
91B50 General equilibrium theory
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