Riemann Surfaces and Algebraic Curves: A First Course in Hurwitz Theory

ISBN-13: 9781316603529 / Angielski / Miękka / 2016 / 194 str.

Renzo Cavalieri; Eric Miles

Opis

Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.

Recenzje

'To wit, the book is indeed well-suited to advanced undergraduates who know some serious algebra, analysis (complex analysis in particular), and are disposed to hit themes in algebraic topology and (to a limited degree) algebraic geometry. It would make a good text for a senior seminar.' Michael Berg, MAA Reviews

Spis treści

Introduction; 1. From complex analysis to Riemann surfaces; 2. Introduction to manifolds; 3. Riemann surfaces; 4. Maps of Riemann surfaces; 5. Loops and lifts; 6. Counting maps; 7. Counting monodromy representations; 8. Representation theory of Sd; 9. Hurwitz numbers and Z(Sd); 10. The Hurwitz potential; Appendix A. Hurwitz theory in positive characteristic; Appendix B. Tropical Hurwitz numbers; Appendix C. Hurwitz spaces; Appendix D. Does physics have anything to say about Hurwitz numbers?; References; Index.