On the gonality of certain quotient varieties

Jonah Leshin

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arXiv · 1309.6230

On the gonality of certain quotient varieties

Jonah Leshin

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Abstract

Noether's problem asks whether, for a given field K and finite group G, the fixed field L := K(x_h : h \in G)^G is a purely transcendental extension of K, where G acts on the x_h by gx_h = x_gh. The field L is naturally the function field of a quotient variety V := V (K,G). In analogy to the case of curves, we define the gonality of V to be the minimal degree of a dominant rational map from V to projective space, which, in a sense, measures the extent to which L may fail to be purely transcendental over K. When G is abelian, we give bounds for the gonality of V (K; G).

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Jonah Leshin. 2013-09-24. On the gonality of certain quotient varieties. https://arxiv.org/abs/1309.6230

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