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Symmetric and alternating groups as monodromy groups of Riemann surfaces. I. Generic covers and covers with many branch points: with an Appendix by R. Guralnick and R. Stafford

About this Title

Robert M. Guralnick and John Shareshian

Publication: Memoirs of the American Mathematical Society
Publication Year: 2007; Volume 189, Number 886
ISBNs: 978-0-8218-3992-8 (print); 978-1-4704-0490-1 (online)
DOI: https://doi.org/10.1090/memo/0886
MathSciNet review: 2343794
MSC: Primary 14H30; Secondary 14H55, 30F20

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Table of Contents

Chapters

  • 1. Introduction and statement of main results
  • 2. Notation and basic lemmas
  • 3. Examples
  • 4. Proving the main results on five or more branch points — Theorems 1.1.1 and 1.1.2
  • 5. Actions on 2-sets — the proof of Theorem 4.0.30
  • 6. Actions on 3-sets — the proof of Theorem 4.0.31
  • 7. Nine or more branch points — the proof of Theorem 4.0.34
  • 8. Actions on cosets of some 2-homogeneous and 3-homogeneous groups
  • 9. Actions on 3-sets compared to actions on larger sets
  • 10. A transposition and an $n$-cycle
  • 11. Asymptotic behavior of $g_k(E)$
  • 12. An $n$-cycle — the proof of Theorem 1.2.1
  • 13. Galois groups of trinomials — the proofs of Propositions 1.4.1 and 1.4.2 and Theorem 1.4.3