Last edited by Talar
Tuesday, July 21, 2020 | History

3 edition of Symmetry Types of Hyperelliptic Riemann Surfaces (Memoires De La Societe Mathematique De France, 86) found in the catalog.

Symmetry Types of Hyperelliptic Riemann Surfaces (Memoires De La Societe Mathematique De France, 86)

E. Bujalance

# Symmetry Types of Hyperelliptic Riemann Surfaces (Memoires De La Societe Mathematique De France, 86)

## by E. Bujalance

Written in English

Subjects:
• Algebra - General,
• Geometry - Algebraic,
• Mathematics,
• Science/Mathematics

• The Physical Object
FormatPaperback
Number of Pages122
ID Numbers
Open LibraryOL12631043M
ISBN 102856291120
ISBN 109782856291122

1. Hyperelliptic-M-Symmetric Riemann Surfaces A closed Riemann surface S of genus g is called M-symmetric if it has a reﬂection ¿: S! S (that is, an anticonformal automor-phism of order two with ﬁxed points) with the maximal number of components of ﬁxed points, that is (g + 1) componets. We also say that ¿ is a M-symmetry. Symmetry Types of Hyperelliptic Riemann Surfaces (Memoires De LA Societe Mathematique De France, 86): ISBN () Softcover, Societe Mathematique De France, Founded in , has become a leading book price comparison site.

Each hyperelliptic surface (S, σ) branched over 2 ⌊ n / 2 ⌋ + 2 points can be realized by a simple centrally symmetric planar 2n-gon P S with opposite sides glued by translation. For an open set of full measure in the parameter space of hyperelliptic surfaces, P S can be taken convex. Represent the hyperelliptic surface (S, σ) underlying. The Riemann Theta Function.- VI The Theta Functions Associated with a Riemann Surface.- VI The Theta Divisor.- VII Examples.- VII. 1. Hyperelliptic Surfaces (Once Again).- VII Relations Among Quadratic Differentials.- VII Examples of Non-hyperelliptic Surfaces.- VII Branch Points of Hyperelliptic Surfaces as Holomorphic Functions.

0. In particular they determined the symmetry types of any p-hyperelliptic Riemann surface of genus g>4p+ 1. We show that their results can be applied for gin range 3p+1symmetry and p-hyperelliptic involution commute if gis even while for odd g, except g=3p+2andp≡1(4),Xalways admits some conformal involution. 1 Preliminaries Number of Conjugacy Classes of Symmetries Counting Ovals of Symmetries Symmetry Types of some Families of Riemann Surfaces Symmetry Types of Riemann Surfaces with a Large Group of Automorphisms Appendix. Series Title: Lecture notes in mathematics (Springer-Verlag), Responsibility: Emilio Bujalance [and.

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### Symmetry Types of Hyperelliptic Riemann Surfaces (Memoires De La Societe Mathematique De France, 86) by E. Bujalance Download PDF EPUB FB2

Symmetry types of hyperelliptic Riemann surfaces. Symmetry types of hyperelliptic algebraic curves of class I. Symmetry types of hyperelliptic algebraic curves of class II. Symmetry types of hyperelliptic algebraic curves of class III. Symmetry types of hyperelliptic algebraic curves of class IV.

calculated the 18 symmetry types of symmetric Riemann surfaces of genus 2. Since all such surfaces are hyperelliptic, these symmetry types appear naturally in this memoir. Symmetry Types of Hyperelliptic Riemann Surfaces The aim of the publication is to present classification of all real structures of hyper-elliptic Riemann surfaces, together with their full group of analytic and antianalytic automorphisms, their topological invariants, their description in terms of polynomials equations and explicit formulae for the corresponding real structures.

Tipo de documento: Artículo: Palabras clave: Riemann surface, symmetry, automorphism group, real form, real algebraic curve: Materias: Ciencias > Matemáticas > ÁlgebraCited by: Symmetry types of hyperelliptic Riemann surfaces By E. Bujalance, F.J. Cirre, J. Gamboa and G.

Gromadzki Download PDF (2 MB). A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if it admits a conformal involution p, called a p-hyperelliptic involution, for which X/p is an orbifold of genus p.

Symmetry t yp es of pq-hyperell iptic Riemann surfaces Let X = H / Γ be a pq -hyp erellipt ic Riemann surface of gen us g> 3 q +1 for some q> p.B y T h e o r e m 3.

7i n[ 7 ], p -a n d q -i n. Topological types of symmetries of elliptic-hyperelliptic Riemann surfaces and an application to moduli spaces. The symmetry type of a Riemann surface, Proc. London Math. Soc., 51, – This monograph deals with symmetries of compact Riemann surfaces.

A symmetry of a compact Riemann surface S is an antianalytic involution of S. It is well known that Riemann surfaces exhibiting symmetry correspond to algebraic curves which can be defined over the field of real numbers. In this. Abstract. LetX be a Riemann surface of surfaceX is called elliptic-hyperelliptic if it admits a conformal involutionh such that the orbit spaceX/〈h〉 has genus involutionh is then called an elliptic-hyperelliptic involution.

Ifg>5 then the involutionh is unique, see [A]. We call symmetry to any anticonformal involution ± (X) be the group of conformal and. The complex plane C is the most basic Riemann surface. The map f(z) = z (the identity map) defines a chart for C, and {f} is an atlas for map g(z) = z * (the conjugate map) also defines a chart on C and {g} is an atlas for charts f and g are not compatible, so this endows C with two distinct Riemann surface structures.

In fact, given a Riemann surface X and its atlas A, the. However, if a Riemann surface Fg admits a symmetry S1 with k mirrors then work of Bujalance and Costa [1] and Natanzon [9] on symmetries with g+1 mirrors suggest that there may possibly be.

An exceptional point in the moduli space of compact Riemann surfaces is a unique surface class whose full automorphism group acts with a triangular signature. A surface admitting a conformal. Abelian diﬀerentials, periods on Riemann surfaces, meromorphic functions, theta functions, and uniformization techniques.

Motivated by the concrete point of view on Riemann surfaces of this book we choose essentially an analytic presentation. Concrete analytic tools and constructions available on Riemann surfaces and their applications to the.

Bujalance, F. Cirre, J. Gamboa and G. Gromadzki, Symmetry types of hyperelliptic Riemann surfaces, Mémoires de la Société Mathématique de France.

Nouvelle Série 86 (). Google Scholar. enabled the groups of automorphisms for hyperelliptic surfaces to be determined later in [6], for elliptic-hyperelliptic surfaces in [15], and for 2-hyperelliptic surfaces in [16].

The groups of automorphisms of cyclic trigonal Riemann surfaces and cyclic p-gonal Riemann surfaces were studied in. It turns out that all such Klein surfaces are dif- ferent real forms of the same family of Riemann surfaces, namely, the family of Riemann surfaces with maximal dihedral symmetry.

Case g even The maximal order of a cyclic group of automorphisms that a Klein surface of even algebraic genus g may admit is 2g + 2, see [5,17]. Let X be a compact Riemann surface of genus $$g \ge 2$$ that possesses a fixed point free group H of automorphisms and let $$Y=X/H$$ denote the orbit space of X under the action of Y possesses a symmetry $$\sigma,$$ that is, an anticonformal involution.

We give conditions that determine when $$\sigma$$ lifts to an anticonformal automorphism of the surface X.

Symmetry types of hyperelliptic Riemann surfaces. By Emilio Bujalance, Francisco-Javier Cirre, J.-M. Gamboa and Grzegorz Gromadzki. Get PDF (2 MB) Year: OAI identifier: oai::MSMF__2_86__1_0 Provided by: Numérisation de Documents.

Let S be a compact Riemann surface of genus g > 1, and let τ: S → S be any anti-conformal automorphism of S, of order an anti-conformal involution is known as a symmetry of S, and the species of all conjugacy classes of all symmetries of S constitute what is known as the symmetry type of surface S is said to have maximal real symmetry if it admits a symmetry τ: S → S.

Preliminaries.- On the Number of Conjugacy Classes of Symmetries of Riemann Surfaces.- Counting Ovals of Symmetries of Riemann Surfaces.- Symmetry Types of Some Families of Riemann Surfaces.- Symmetry Types of Riemann Surfaces with a Large Group of Automorphisms.

Series Title: Lecture notes in mathematics, Responsibility. Symmetry is a classic study of symmetry in mathematics, the sciences, nature, and art from one of the twentieth century's greatest mathematicians. Hermann Weyl explores the concept of symmetry beginning with the idea that it represents a harmony of proportions, and gradually departs to examine its more abstract varieties and manifestations―as bilateral, translatory, rotational, Reviews: I'm a beginner and I only know the basic definition of a hyperelliptic surface, namely admitting a 2-fold holomorphic mapping onto $\mathbb{P}^1$.

Is there any further properties of hyperelliptic surfaces that I can use to tackle this problem?