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The equivalence classes of holomorphic mappings of genus 3 Riemann surfaces onto genus 2 Riemann surfaces

Описание

Тип публикации: статья из журнала

Год издания: 2016

Идентификатор DOI: 10.1134/S0037446616060124

Ключевые слова: anticonformal involution, conformal automorphism, holomorphic mapping, real curve, Riemann surface

Аннотация: Denote the set of all holomorphic mappings of a genus 3 Riemann surface S3onto a genus 2 Riemann surface S2by Hol(S3, S2). Call two mappings f and g in Hol(S3, S2) equivalent whenever there exist conformal automorphisms ? and ? of S3and S2respectively with f ? ? = ? ? g. It is known that Hol(S3, S2) always consists of at most two eПоказать полностьюquivalence classes. We obtain the following results: If Hol(S3, S2) consists of two equivalence classes then both S3and S2can be defined by real algebraic equations; furthermore, for every pair of inequivalent mappings f and g in Hol(S3, S2) there exist anticonformal automorphisms ?? and ?? with f ? ?? = ?? ? g. Up to conformal equivalence, there exist exactly three pairs of Riemann surfaces (S3, S2) such that Hol(S3, S2) consists of two equivalence classes. © 2016, Pleiades Publishing, Ltd.

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Издание

Журнал: Siberian Mathematical Journal

Выпуск журнала: Vol. 57, Is. 6

Номера страниц: 1055-1065

Персоны

  • Mednykh A.D. (Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk Siberian Federal University, Krasnoyarsk, Russian Federation)
  • Mednykh I.A. (Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk Siberian Federal University, Krasnoyarsk, Russian Federation)

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