Enriques Involutions and Brauer Classes

Research output: Contribution to journal › Article › Research › peer review

Authors

  • A. N. Skorobogatov
  • D. Valloni

Research Organisations

External Research Organisations

  • Imperial College London
  • Russian Academy of Sciences (RAS)
View graph of relations

Details

Original languageEnglish
Pages (from-to)606-621
Number of pages16
JournalNagoya mathematical journal
Volume251
Early online date13 Dec 2022
Publication statusPublished - Sept 2023

Abstract

We prove that every element of order 2 in the Brauer group of a complex Kummer surface X descends to an Enriques quotient of X. In generic cases, this gives a bijection between the set of Enriques quotients of X up to isomorphism and the set of Brauer classes of X of order 2. For some K3 surfaces of Picard rank we prove that the fibers of above the nonzero points have the same cardinality.

ASJC Scopus subject areas

Cite this

Enriques Involutions and Brauer Classes. / Skorobogatov, A. N.; Valloni, D.
In: Nagoya mathematical journal, Vol. 251, 09.2023, p. 606-621.

Research output: Contribution to journal › Article › Research › peer review

Skorobogatov AN, Valloni D. Enriques Involutions and Brauer Classes. Nagoya mathematical journal. 2023 Sept;251:606-621. Epub 2022 Dec 13. doi: 10.48550/arXiv.2202.08030, 10.1017/nmj.2022.43
Skorobogatov, A. N. ; Valloni, D. / Enriques Involutions and Brauer Classes. In: Nagoya mathematical journal. 2023 ; Vol. 251. pp. 606-621.
Download
@article{45d013afb9e04cde8d7be52519eb23bd,
title = "Enriques Involutions and Brauer Classes",
abstract = "We prove that every element of order 2 in the Brauer group of a complex Kummer surface X descends to an Enriques quotient of X. In generic cases, this gives a bijection between the set of Enriques quotients of X up to isomorphism and the set of Brauer classes of X of order 2. For some K3 surfaces of Picard rank we prove that the fibers of above the nonzero points have the same cardinality.",
author = "Skorobogatov, {A. N.} and D. Valloni",
note = "Funding Information: D.V. was funded by the European Research Council under EU Horizon 2020 research and innovation program grant agreement no. 948066. ",
year = "2023",
month = sep,
doi = "10.48550/arXiv.2202.08030",
language = "English",
volume = "251",
pages = "606--621",
journal = "Nagoya mathematical journal",
issn = "0027-7630",
publisher = "Cambridge University Press",

}

Download

TY - JOUR

T1 - Enriques Involutions and Brauer Classes

AU - Skorobogatov, A. N.

AU - Valloni, D.

N1 - Funding Information: D.V. was funded by the European Research Council under EU Horizon 2020 research and innovation program grant agreement no. 948066.

PY - 2023/9

Y1 - 2023/9

N2 - We prove that every element of order 2 in the Brauer group of a complex Kummer surface X descends to an Enriques quotient of X. In generic cases, this gives a bijection between the set of Enriques quotients of X up to isomorphism and the set of Brauer classes of X of order 2. For some K3 surfaces of Picard rank we prove that the fibers of above the nonzero points have the same cardinality.

AB - We prove that every element of order 2 in the Brauer group of a complex Kummer surface X descends to an Enriques quotient of X. In generic cases, this gives a bijection between the set of Enriques quotients of X up to isomorphism and the set of Brauer classes of X of order 2. For some K3 surfaces of Picard rank we prove that the fibers of above the nonzero points have the same cardinality.

UR - http://www.scopus.com/inward/record.url?scp=85170849513&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2202.08030

DO - 10.48550/arXiv.2202.08030

M3 - Article

AN - SCOPUS:85170849513

VL - 251

SP - 606

EP - 621

JO - Nagoya mathematical journal

JF - Nagoya mathematical journal

SN - 0027-7630

ER -