# Computational Algebraic and Analytic Geometry

Share this page *Edited by *
*Mika Seppälä; Emil Volcheck*

Algebraic, analytic, and geometric methods are used to study
algebraic curves and Riemann surfaces from a variety of points of
view. The object of the study is the same. The methods are
different. The fact that a multitude of methods, stemming from very
different mathematical cultures, can be used to study the same objects
makes this area both fascinating and challenging.

# Table of Contents

## Computational Algebraic and Analytic Geometry

- Preface vii8 free
- Large hyperbolic polygons and hyperelliptic Riemann surfaces 110 free
- On isolated strata of pentagonal Riemann surfaces in the branch locus of moduli spaces 1928
- Finite group actions of large order on compact bordered surfaces 2534
- 1. Introduction 2534
- 2. Preliminaries 2736
- 3. Signatures associated with groups of order ≥6(𝑔-1) 2837
- 4. A computational approach 3039
- 5. Finite group actions of order 12(𝑔-1) 3241
- 6. Finite group actions of order 8(𝑔-1) 3443
- 7. Finite group actions of order (20)/3(𝑔-1) 4150
- 8. Finite group actions of order 6(𝑔-1) 4251
- 9. Infinite families 5362
- References 5564

- Surfaces of low degree containing a canonical curve 5766
- Ideals of curves given by points 7180
- Non-genera of curves with automorphisms in characteristic 𝑝 8998
- Numerical Schottky uniformizations of certain cyclic L-gonal curves 97106
- Generalized lantern relations and planar line arrangements 113122
- Effective 𝑝-adic cohomology for cyclic cubic threefolds 127136
- 1. Zeta functions: generalities 128137
- 2. Algebraic de Rham cohomology 136145
- 3. de Rham cohomology and 𝑝-adic cohomology 139148
- 4. The direct method for cyclic cubic threefolds 143152
- 5. Picard-Fuchs-Manin connections 147156
- 6. The deformation method for cyclic cubic threefolds 153162
- Appendix A. Notes and further reading 163172
- References 167176

- Generating sets of affine groups of low genus 173182
- Classification of algebraic ODEs with respect to rational solvability 193202
- Circle packings on conformal and affine tori 211220
- Effective radical parametrization of trigonal curves 221230