On ℤ/3-Godeaux Surfaces

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Stephen Coughlan
  • Giancarlo Urzúa

Organisationseinheiten

Externe Organisationen

  • Pontificia Universidad Catolica de Chile
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis)5609-5637
Seitenumfang29
FachzeitschriftInternational Mathematics Research Notices
Jahrgang2018
Ausgabenummer18
Frühes Online-Datum20 März 2017
PublikationsstatusVeröffentlicht - Sept. 2018

Abstract

We prove that Godeaux-Reid surfaces with torsion group ℤ/3 have topological fundamental group ℤ/3. For this purpose, we describe degenerations to stable KSBA surfaces with one 1/4 (1, 1) singularity, whose minimal resolution are elliptic fibrations with two multiplicity three fibres and one I4 singular fibre. We study special such degenerations which have an involution, describing the corresponding Campedelli double plane construction. We also find some stable rational degenerations, some of which have more singularities, and one of which has a single 1/9 (1, 2) singularity, the minimal possible index for such a surface. Finally, we do the analogous study for the Godeaux surfaces with torsion ℤ/4.

Zitieren

On ℤ/3-Godeaux Surfaces. / Coughlan, Stephen; Urzúa, Giancarlo.
in: International Mathematics Research Notices, Jahrgang 2018, Nr. 18, 09.2018, S. 5609-5637.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Coughlan S, Urzúa G. On ℤ/3-Godeaux Surfaces. International Mathematics Research Notices. 2018 Sep;2018(18):5609-5637. Epub 2017 Mär 20. doi: 10.48550/arXiv.1609.02177, 10.1093/imrn/rnx049
Coughlan, Stephen ; Urzúa, Giancarlo. / On ℤ/3-Godeaux Surfaces. in: International Mathematics Research Notices. 2018 ; Jahrgang 2018, Nr. 18. S. 5609-5637.
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