Computational algebraic and analytic geometry : AMS special sessions on computational algebraic and analytic geometry for low-dimensional varieties, January 8, 2007, New Orleans, LA, January 6, 2009, Washington, DC, January 6, 2011, New Orleans, LA / Mika Seppala, Emil Volcheck, editors.

Format:

Book

Contributor:

Seppälä, Mika, editor.

Volcheck, Emil, 1966- editor.

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 572

Contemporary mathematics, 572 0271-4132

Language:

English

Subjects (All):

Curves, Algebraic--Data processing--Congresses.

Curves, Algebraic.

Riemann surfaces--Congresses.

Riemann surfaces.

Physical Description:

1 online resource (242 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2012]

Language Note:

English

Summary:

This volume contains the proceedings of three AMS Special Sessions on Computational Algebraic and Analytic Geometry for Low-Dimensional Varieties held January 8, 2007, in New Orleans, LA; January 6, 2009, in Washington, DC; and January 6, 2011, in New Orleans, LA. 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.

Contents:

Preface

Large hyperbolic polygons and hyperelliptic Riemann surfaces

1. Hyperbolic Polygons

2. Closing large polygons

3. Groups from Polygons

4. Reduction Algorithms on Polygons

References

On isolated strata of pentagonal Riemann surfaces in the branch locus of moduli spaces

1. Introduction

2. Riemann surfaces and Fuchsian groups

3. Disconnectedness by pentagonal Riemann surfaces

Finite group actions of large order on compact bordered surfaces

2. Preliminaries

2. Border bases for homogeneous ideals

3. Curves given by points

4. Curves in X given by approximate points

5. Degree bounds for ideal generators

Acknowledgments

Non-genera of curves with automorphisms in characteristic

2. Non-genera for -actions

3. -ranks

Numerical Schottky uniformizations of certain cyclic L-gonal curves

3. Basic facts on Whittaker groups

4. Basic objects

5. The generalized Myrberg's algorithm

6. Application to algebraic curves

Acknowledgements

Generalized lantern relations and planar line arrangements

2. Real line arrangements and relations on Dehn twists

3. Applications

Effective -adic cohomology for cyclic cubic threefolds

1. Zeta functions: generalities

2. Algebraic de Rham cohomology

3. de Rham cohomology and -adic cohomology

4. The direct method for cyclic cubic threefolds

5. Picard-Fuchs-Manin connections

6. The deformation method for cyclic cubic threefolds

Appendix A. Notes and further reading

Generating sets of affine groups of low genus

2. The Algorithm

3. Genus Zero Systems and the Guralnick-Thompson Conjecture

Classification of algebraic ODEs with respect to rational solvability

3. A group of affine linear transformations

4. Solvable AODEs and their associated systems

5. Parametrizable ODEs with special geometric shapes

6. Conclusion

References.

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-8989-3