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A note on large automorphism groups of compact Riemann surfaces
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-9557-9566
Univ La Frontera, Chile.
2020 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 547Article in journal (Refereed) Published
Abstract [en]

Belolipetsky and Jones classified those compact Riemann surfaces of genus g admitting a large group of automorphisms of order lambda(g - 1), for each lambda amp;gt; 6, under the assumption that g - 1 is a prime number. In this article we study the remaining large cases; namely, we classify Riemann surfaces admitting 5(g - 1) and 6(g - 1) automorphisms, with g - 1 a prime number. As a consequence, we obtain the classification of Riemann surfaces admitting a group of automorphisms of order 3(g - 1), with g - 1 a prime number. We also provide isogeny decompositions of their Jacobian varieties. (C) 2019 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2020. Vol. 547
Keywords [en]
Riemann surfaces; Group actions; Jacobian varieties
National Category
Geometry
Identifiers
URN: urn:nbn:se:liu:diva-163646DOI: 10.1016/j.jalgebra.2019.11.012ISI: 000509419000001OAI: oai:DiVA.org:liu-163646DiVA, id: diva2:1394215
Note

Funding Agencies|Redes Etapa Inicial Grant [2017-170071]; FONDECYTComision Nacional de Investigacion Cientifica y Tecnologica (CONICYT)CONICYT FONDECYT [11180024, 1190991]; PIA-CONICYT Grant [Anillo ACT1415]

Available from: 2020-02-18 Created: 2020-02-18 Last updated: 2020-03-13

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The full text will be freely available from 2021-11-26 15:46
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