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arXiv · 2610.15487

Rationality of Kontsevich moduli of stable maps, and their Galois descents

Jaya NN Iyer
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Abstract

Let k be a field and X be a geometrically rational variety over k. We investigate the Kontsevich moduli spaces of genus zero, stable maps with curve classes of low degree on X over k, and define their twisted Galois descents. We study the k-rationality of these spaces in detail when X is a projective space/Severi Brauer variety and when X is moduli of genus zero n-marked points. When X is a homogeneous variety over the field of complex numbers, this is a well-known theorem of Kim-Pandharipande.

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Jaya NN Iyer. 2026-10-11. Rationality of Kontsevich moduli of stable maps, and their Galois descents. https://arxiv.org/abs/2610.15487

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