[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.
Accepté le :
Publié le :
Annelies Jaspers 1
@article{CRMATH_2017__355_2_200_0,
author = {Annelies Jaspers},
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},
}
Annelies Jaspers. The global monodromy property for K3 surfaces allowing a triple-point-free model. Comptes Rendus. Mathématique, Volume 355 (2017) no. 2, pp. 200-204. doi : 10.1016/j.crma.2016.12.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.12.002/
[1] Computing motivic zeta functions on log smooth models, 2016 | arXiv
[2] Triple-point-free degenerations of surfaces with Kodaira number zero, The Birational Geometry of Degenerations, Prog. Math., vol. 29, Birkhäuser, Basel, Switzerland, 1983, pp. 353-386
[3] Geometry on arc spaces of algebraic varieties, Barcelona, Spain, 10–14 July 2000 (Prog. Math.), Volume vol. 201, Birkhäuser, Basel, Switzerland (2001), pp. 327-348
[4] Motivic zeta functions of abelian varieties, and the monodromy conjecture, Adv. Math., Volume 227 (2011), pp. 610-653
[5] Motivic zeta functions for degenerations of abelian varieties and Calabi–Yau varieties (A. Campillo et al., eds.), Recent Trends on Zeta Functions in Algebra and Geometry, Contemp. Math., vol. 566, American Mathematical Society, 2012, pp. 233-259
[6] L.H. Halle, J. Nicaise, Motivic zeta functions of degenerating Calabi–Yau varieties, in preparation.
[7] The global monodromy property for K3 surfaces allowing a triple point free model, KU Leuven/University of Copenhagen, Belgium/Denmark, 2017 PhD thesis (in press)
[8] An introduction to p-adic and motivic zeta functions and the monodromy conjecture (G. Bhowmik; K. Matsumoto; H. Tsumura, eds.), Algebraic and Analytic Aspects of Zeta Functions and L-Functions, MSJ Mem., vol. 21, Mathematical Society of Japan, 2010, pp. 115-140
[9] The motivic Serre invariant, ramification, and the analytic Milnor fiber, Invent. Math., Volume 168 (2007) no. 1, pp. 133-173
[10] The Grothendieck ring of varieties (R. Cluckers; J. Nicaise; J. Sebag, eds.), Motivic Integration and Its Interactions with Model Theory and Non-Archimedean Geometry, Lond. Math. Soc. Lect. Notes Ser., vol. 383, Cambridge University Press, Cambridge, UK, 2011, pp. 145-188
- Motivic zeta functions of the Hilbert schemes of points on a surface, Documenta Mathematica, Volume 29 (2024) no. 4, pp. 763-804 | DOI:10.4171/dm/948 | Zbl:1551.14072
- Lefschetz numbers of Verdier monodromy and the motivic monodromy conjecture for toric varieties, Illinois Journal of Mathematics, Volume 67 (2023) no. 4, pp. 663-675 | DOI:10.1215/00192082-10950709 | Zbl:1541.14002
- What is the monodromy property for degenerations of Calabi-Yau varieties?, Birational geometry and moduli spaces. Selected papers presented at the INdAM workshop, Rome, Italy, June 11–15, 2018, Cham: Springer, 2020, pp. 133-150 | DOI:10.1007/978-3-030-37114-2_8 | Zbl:1442.14128
- Motivic zeta functions of degenerating Calabi-Yau varieties, Mathematische Annalen, Volume 370 (2018) no. 3-4, pp. 1277-1320 | DOI:10.1007/s00208-017-1578-3 | Zbl:1400.14045
- The global monodromy property for
Cité par 5 documents. Sources : zbMATH
Commentaires - Politique