Quartic surfaces, their bitangents and rational points
Épijournal de Géométrie Algébrique, Tome 7 (2023)
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Let X be a smooth quartic surface not containing lines, defined over a number field K. We prove that there are only finitely many bitangents to X which are defined over K. This result can be interpreted as saying that a certain surface, having vanishing irregularity, contains only finitely many rational points. In our proof, we use the geometry of lines of the quartic double solid associated to X. In a somewhat opposite direction, we show that on any quartic surface X over a number field K, the set of algebraic points in X(K) which are quadratic over a suitable finite extension K' of K is Zariski-dense.
@article{10_46298_epiga_2022_8987,
author = {Corvaja, Pietro and Zucconi, Francesco},
title = {Quartic surfaces, their bitangents and rational points},
journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
publisher = {mathdoc},
volume = {7},
year = {2023},
doi = {10.46298/epiga.2022.8987},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2022.8987/}
}
TY - JOUR AU - Corvaja, Pietro AU - Zucconi, Francesco TI - Quartic surfaces, their bitangents and rational points JO - Épijournal de Géométrie Algébrique PY - 2023 VL - 7 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.46298/epiga.2022.8987/ DO - 10.46298/epiga.2022.8987 LA - en ID - 10_46298_epiga_2022_8987 ER -
%0 Journal Article %A Corvaja, Pietro %A Zucconi, Francesco %T Quartic surfaces, their bitangents and rational points %J Épijournal de Géométrie Algébrique %D 2023 %V 7 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.46298/epiga.2022.8987/ %R 10.46298/epiga.2022.8987 %G en %F 10_46298_epiga_2022_8987
Corvaja, Pietro; Zucconi, Francesco. Quartic surfaces, their bitangents and rational points. Épijournal de Géométrie Algébrique, Tome 7 (2023). doi: 10.46298/epiga.2022.8987
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