Topology of algebraic curves : an approach via dessins d'enfants / Alex Degtyarev.

By:

Degtyarev, A. (Alexander), 1962- [author.]

Material type: Text

text

Media type:

computer

Carrier type:

online resource

ISBN:

9783110258424
3110258420
9783110258424
9783112204122
3112204123
9786613940186
6613940186
1283627736
9781283627733

Subject(s): Genre/Form:

Additional physical formats: Print version:: No titleDDC classification:

516.3/52 23

LOC classification:

QA567

Other classification:

SK 240

Online resources:

Click here to access online

Contents:

Frontmatter -- Preface -- Contents -- Part I. Skeletons and dessins -- Chapter 1. Graphs -- Chapter 2. The groups [Gamma] and B3 -- Chapter 3. Trigonal curves and elliptic surfaces -- Chapter 4. Dessins -- Chapter 5. The braid monodromy -- Part II. Applications -- Chapter 6. The metabelian invariants -- Chapter 7. A few simple computations -- Chapter 8. Fundamental groups of plane sextics -- Chapter 9. The transcendental lattice -- Chapter 10. Monodromy factorizations -- Appendices -- Appendix A. An algebraic complement -- Appendix B. Bigonal curves in [Sigma]d -- Appendix C. Computer implementations -- Appendix D. Definitions and notation -- Bibliography -- Index of figures -- Index of tables -- Index.

Summary: The book summarizes the state and new results on the topology of trigonal curves in geometrically ruled surfaces. Emphasis is placed upon various applications of the theory to related areas, most notably singularplane curves of small degree, elliptic surfaces, and Lefschetz fibrations (both complex and real), and Hurwitz equivalence of braid monodromy factorizations. The monograph conveys recent knowledge about related objects and is of interest to researchers and graduate students in the fields of topology and of complex and real algebraic varieties.

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Includes bibliographical references (pages 369-378) and indexes.

The book summarizes the state and new results on the topology of trigonal curves in geometrically ruled surfaces. Emphasis is placed upon various applications of the theory to related areas, most notably singularplane curves of small degree, elliptic surfaces, and Lefschetz fibrations (both complex and real), and Hurwitz equivalence of braid monodromy factorizations. The monograph conveys recent knowledge about related objects and is of interest to researchers and graduate students in the fields of topology and of complex and real algebraic varieties.

In English.

880-01 Frontmatter -- Preface -- Contents -- Part I. Skeletons and dessins -- Chapter 1. Graphs -- Chapter 2. The groups [Gamma] and B3 -- Chapter 3. Trigonal curves and elliptic surfaces -- Chapter 4. Dessins -- Chapter 5. The braid monodromy -- Part II. Applications -- Chapter 6. The metabelian invariants -- Chapter 7. A few simple computations -- Chapter 8. Fundamental groups of plane sextics -- Chapter 9. The transcendental lattice -- Chapter 10. Monodromy factorizations -- Appendices -- Appendix A. An algebraic complement -- Appendix B. Bigonal curves in [Sigma]d -- Appendix C. Computer implementations -- Appendix D. Definitions and notation -- Bibliography -- Index of figures -- Index of tables -- Index.

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