Smooth covers of moduli stacks of Riemann surfaces with symmetry

Bollettino dell Unione Matematica Italiana ◽

10.1007/s40574-021-00284-7 ◽

2021 ◽

Author(s):

Fabio Perroni

Keyword(s):

Riemann Surfaces ◽

Projective Variety ◽

Finite Cover ◽

Moduli Stacks ◽

Moduli Stack ◽

Compact Riemann Surfaces ◽

Group Of Symmetries

AbstractWe construct explicitly a finite cover of the moduli stack of compact Riemann surfaces with a given group of symmetries by a smooth quasi-projective variety.

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Complete set of Genera of Compact Riemann Surfaces with reference to the point Group of Sulphur (S8) Molecule

Journal of Ultra Scientist of Physical Sciences Section A ◽

10.22147/jusps-a/320701 ◽

2020 ◽

Vol 32 (7) ◽

pp. 88-92

Author(s):

RAFIQUL ISLAM ◽

◽

CHANDRA CHUTIA ◽

Keyword(s):

Automorphism Group ◽

Riemann Surfaces ◽

Point Group ◽

Finite Point ◽

Group Of Automorphisms ◽

Complete Set ◽

Compact Riemann Surfaces ◽

Group Of Symmetries

In this paper we consider the group of symmetries of the Sulphur molecule (S8 ) which is a finite point group of order 16 denote by D16 generated by two elements having the presentation { u\upsilon/u2= \upsilon8 = (u\upsilon)2 = 1} and find the complete set of genera (g ≥ 2) of Compact Riemann surfaces on which D16 acts as a group of automorphisms as follows: D16 the group of symmetries of the sulphur (S8) molecule of order 16 acts as an automorphism group of a compact Riemann surfaces of genus g ≥ 2 if and only if there are integers \lambda and \mu such that \lambda \leq 1 and \mu \geq 1 and g=\lambda +8\mu (\geq2) , \mu\geq |\lambda|

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On complete curves in moduli space I

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100070535 ◽

1991 ◽

Vol 110 (3) ◽

pp. 461-466 ◽

Cited By ~ 4

Author(s):

Gabino González Díez ◽

William J. Harvey

Keyword(s):

Moduli Space ◽

General Position ◽

Riemann Surfaces ◽

Projective Variety ◽

Dimension 2 ◽

Compact Riemann Surfaces ◽

Set Of Points

Letgdenote the moduli space of compact Riemann surfaces of genusg> 3. It is known thatgis a non-complete quasi-projective variety that contains many complete curves. This is because the Satake compactificationgofgis projective and the boundary\has co-dimension 2; thus by intersectingwith hypersurfaces in sufficiently general position one obtains a complete curve ingpassing through any given set of points [8].

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A Hodge theoretic projective structure on compact Riemann surfaces

Journal de Mathématiques Pures et Appliquées ◽

10.1016/j.matpur.2021.02.005 ◽

2021 ◽

Vol 149 ◽

pp. 1-27

Author(s):

Indranil Biswas ◽

Elisabetta Colombo ◽

Paola Frediani ◽

Gian Pietro Pirola

Keyword(s):

Riemann Surfaces ◽

Projective Structure ◽

Compact Riemann Surfaces

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Convergence of Discrete Period Matrices and Discrete Holomorphic Integrals for Ramified Coverings of the Riemann Sphere

Mathematical Physics Analysis and Geometry ◽

10.1007/s11040-021-09394-2 ◽

2021 ◽

Vol 24 (3) ◽

Author(s):

Alexander I. Bobenko ◽

Ulrike Bücking

Keyword(s):

Error Estimate ◽

Branch Point ◽

Riemann Surfaces ◽

Riemann Sphere ◽

Holomorphic Functions ◽

Convergence Result ◽

Edge Length ◽

Ramified Covering ◽

Compact Riemann Surfaces ◽

Ramified Coverings

AbstractWe consider the class of compact Riemann surfaces which are ramified coverings of the Riemann sphere $\hat {\mathbb {C}}$ ℂ ̂ . Based on a triangulation of this covering we define discrete (multivalued) harmonic and holomorphic functions. We prove that the corresponding discrete period matrices converge to their continuous counterparts. In order to achieve an error estimate, which is linear in the maximal edge length of the triangles, we suitably adapt the triangulations in a neighborhood of every branch point. Finally, we also prove a convergence result for discrete holomorphic integrals for our adapted triangulations of the ramified covering.

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