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Connecting p-gonal loci in the compactification of moduli space
Departamento de Matematicas Fundamentales, UNED.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9557-9566
Department of Mathematics, University of Fribourg, Switzerland.
2015 (English)In: Revista Matemática Complutense, ISSN 1139-1138, Vol. 28, no 2, 469-486 p.Article in journal (Refereed) Published
Abstract [en]

Consider the moduli space M g of Riemann surfaces of genusg≥2 and its Deligne-Munford compactification M g ¯ . We are interested in the branch locus B g for g>2 , i.e., the subset of M g consisting of surfaces with automorphisms. It is well-known that the set of hyperelliptic surfaces (the hyperelliptic locus) is connected in M g but the set of (cyclic) trigonal surfaces is not. By contrast, we show that for g≥5 the set of (cyclic) trigonal surfaces is connected in M g ¯ . To do so we exhibit an explicit nodal surface that lies in the completion of every equisymmetric set of 3-gonal Riemann surfaces. For p>3 the connectivity of the p -gonal loci becomes more involved. We show that for p≥11 prime and genus g=p−1 there are one-dimensional strata of cyclic p -gonal surfaces that are completely isolated in the completion B g ¯ of the branch locus in M g ¯ .

Place, publisher, year, edition, pages
Springer, 2015. Vol. 28, no 2, 469-486 p.
National Category
Geometry
Identifiers
URN: urn:nbn:se:liu:diva-115125DOI: 10.1007/s13163-014-0161-7ISI: 000354223100008OAI: oai:DiVA.org:liu-115125DiVA: diva2:793831
Available from: 2015-03-09 Created: 2015-03-09 Last updated: 2015-06-11

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