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Rationality of Kontsevich moduli of stable maps, and their Galois descents
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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BibTeX
@misc{iyer2026rationality,
title = {{Rationality of Kontsevich moduli of stable maps, and their Galois descents}},
author = {Jaya NN Iyer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15487},
eprint = {2610.15487},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15487},
}
RIS
TY - UNPB
TI - Rationality of Kontsevich moduli of stable maps, and their Galois descents
AU - Jaya NN Iyer
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15487
UR - https://arxiv.org/abs/2610.15487
AB - 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.
ER -