Symmetric and alternating groups as monodromy groups of Riemann surfaces I : [electronic resource] generic covers and covers with many branch points / Robert M. Guralnick, John Shareshian ; with an appendix by R. Guralnick and J. Stafford.

By: Guralnick, Robert M, 1950-Contributor(s): Shareshian, JohnMaterial type: TextTextSeries: Memoirs of the American Mathematical Society ; v. 886Publication details: Providence, R.I. : American Mathematical Society, c2007Description: 1 online resource (vi, 128 p. : ill.)ISBN: 9781470404901 (online)Subject(s): Permutation groups | Curves | Monodromy groups | Riemann surfaces | Symmetry groupsAdditional physical formats: Symmetric and alternating groups as monodromy groups of Riemann surfaces I :DDC classification: 512/.21 LOC classification: QA175 | .G87 2007Online resources: Contents | Contents
Contents:
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
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Includes bibliographical references (p. 127-128).

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

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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