Rank one sheaves over quaternion algebras on Enriques surfaces

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

Authors

  • Fabian Bernhard Reede

Research Organisations

View graph of relations

Details

Original languageEnglish
Pages (from-to)105-112
Number of pages8
JournalAdvances in Geometry
Volume22
Issue number1
Early online date6 Jul 2021
Publication statusPublished - 27 Jan 2022

Abstract

Let X be an Enriques surface over the field of complex numbers. We prove that there exists a nontrivial quaternion algebra 𝓐 on X. Then we study the moduli scheme of torsion free 𝓐-modules of rank one. Finally we prove that this moduli scheme is an étale double cover of a Lagrangian subscheme in the corresponding moduli scheme on the associated covering K3 surface.

Cite this

Rank one sheaves over quaternion algebras on Enriques surfaces. / Reede, Fabian Bernhard.
In: Advances in Geometry, Vol. 22, No. 1, 27.01.2022, p. 105-112.

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

Reede FB. Rank one sheaves over quaternion algebras on Enriques surfaces. Advances in Geometry. 2022 Jan 27;22(1):105-112. Epub 2021 Jul 6. doi: 10.1515/advgeom-2021-0027
Reede, Fabian Bernhard. / Rank one sheaves over quaternion algebras on Enriques surfaces. In: Advances in Geometry. 2022 ; Vol. 22, No. 1. pp. 105-112.
Download
@article{46612f6a73e140f08bec9094691f236a,
title = "Rank one sheaves over quaternion algebras on Enriques surfaces",
abstract = "Let X be an Enriques surface over the field of complex numbers. We prove that there exists a nontrivial quaternion algebra 퓐 on X. Then we study the moduli scheme of torsion free 퓐-modules of rank one. Finally we prove that this moduli scheme is an {\'e}tale double cover of a Lagrangian subscheme in the corresponding moduli scheme on the associated covering K3 surface.",
author = "Reede, {Fabian Bernhard}",
year = "2022",
month = jan,
day = "27",
doi = "10.1515/advgeom-2021-0027",
language = "English",
volume = "22",
pages = "105--112",
journal = "Advances in Geometry",
issn = "1615-715X",
publisher = "Walter de Gruyter GmbH",
number = "1",

}

Download

TY - JOUR

T1 - Rank one sheaves over quaternion algebras on Enriques surfaces

AU - Reede, Fabian Bernhard

PY - 2022/1/27

Y1 - 2022/1/27

N2 - Let X be an Enriques surface over the field of complex numbers. We prove that there exists a nontrivial quaternion algebra 퓐 on X. Then we study the moduli scheme of torsion free 퓐-modules of rank one. Finally we prove that this moduli scheme is an étale double cover of a Lagrangian subscheme in the corresponding moduli scheme on the associated covering K3 surface.

AB - Let X be an Enriques surface over the field of complex numbers. We prove that there exists a nontrivial quaternion algebra 퓐 on X. Then we study the moduli scheme of torsion free 퓐-modules of rank one. Finally we prove that this moduli scheme is an étale double cover of a Lagrangian subscheme in the corresponding moduli scheme on the associated covering K3 surface.

UR - http://www.scopus.com/inward/record.url?scp=85110137623&partnerID=8YFLogxK

U2 - 10.1515/advgeom-2021-0027

DO - 10.1515/advgeom-2021-0027

M3 - Article

AN - SCOPUS:85110137623

VL - 22

SP - 105

EP - 112

JO - Advances in Geometry

JF - Advances in Geometry

SN - 1615-715X

IS - 1

ER -