[La propriété de monodromie globale pour les surfaces K3 ayant un modèle sans point triple]
Inspirés par la conjecture de monodromie motivique, Halle et Nicaise ont défini la propriété de monodromie globale pour les variétés de Calabi–Yau définies sur un corps de valuation discrète. Dans cette note, nous étudions cette propriété pour les surfaces K3 ayant un modèle sans point triple. Le résultat principal est que la propriété de monodromie globale est satisfaite pour les surfaces K3 ayant une dégénérescence en pot de fleurs. Elle est également satisfaite pour les surfaces K3 ayant une dégénérescence en chaîne sous une condition supplémentaire.
Inspired by the motivic monodromy conjecture, Halle and Nicaise defined the global monodromy property for Calabi–Yau varieties over a discretely valued field. In this note, we discuss this property for K3 surfaces allowing a strict normal crossings model where no three components in the special fiber have a common intersection. The main result is that the global monodromy property holds for a K3 surface with a so-called flowerpot degeneration. It also holds for K3 surfaces with a chain degeneration under certain conditions.
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@article{CRMATH_2017__355_2_200_0,
author = {Jaspers, Annelies},
title = {The global monodromy property for {\protect\emph{K}3} surfaces allowing a triple-point-free model},
journal = {Comptes Rendus. Math\'ematique},
pages = {200--204},
publisher = {Elsevier},
volume = {355},
number = {2},
year = {2017},
doi = {10.1016/j.crma.2016.12.002},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.12.002/}
}
TY - JOUR AU - Jaspers, Annelies TI - The global monodromy property for K3 surfaces allowing a triple-point-free model JO - Comptes Rendus. Mathématique PY - 2017 SP - 200 EP - 204 VL - 355 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.12.002/ DO - 10.1016/j.crma.2016.12.002 LA - en ID - CRMATH_2017__355_2_200_0 ER -
%0 Journal Article %A Jaspers, Annelies %T The global monodromy property for K3 surfaces allowing a triple-point-free model %J Comptes Rendus. Mathématique %D 2017 %P 200-204 %V 355 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.12.002/ %R 10.1016/j.crma.2016.12.002 %G en %F CRMATH_2017__355_2_200_0
Jaspers, Annelies. The global monodromy property for K3 surfaces allowing a triple-point-free model. Comptes Rendus. Mathématique, Tome 355 (2017) no. 2, pp. 200-204. doi : 10.1016/j.crma.2016.12.002. http://www.numdam.org/articles/10.1016/j.crma.2016.12.002/
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