Symmetric and Alternating Groups As Monodromy Groups of Riemann Surfaces 1: Generic Covers and Covers With Many Branch Points (Memoirs of the American Mathematical Society)

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9780821839928: Symmetric and Alternating Groups As Monodromy Groups of Riemann Surfaces 1: Generic Covers and Covers With Many Branch Points (Memoirs of the American Mathematical Society)

The authors consider indecomposable degree $n$ covers of Riemann surfaces with monodromy group an alternating or symmetric group of degree $d$. They show that if the cover has five or more branch points then the genus grows rapidly with $n$ unless either $d = n$ or the curves have genus zero, there are precisely five branch points and $n =d(d-1)/2$. Similarly, if there is a totally ramified point, then without restriction on the number of branch points the genus grows rapidly with $n$ unless either $d=n$ or the curves have genus zero and $n=d(d-1)/2$. One consequence of these results is that if $f:X \rightarrow \mathbb{P 1$ is indecomposable of degree $n$ with $X$ the generic Riemann surface of genus $g \ge 4$, then the monodromy group is $S n$ or $A n$ (and both can occur for $n$ sufficiently large). The authors also show if that if $f(x)$ is an indecomposable rational function of degree $n$ branched at $9$ or more points, then its monodromy group is $A n$ or $S n$.Finally, they answer a question of Elkies by showing that the curve parameterizing extensions of a number field given by an irreducible trinomial with Galois group $H$ has large genus unless $H=A n$ or $S n$ or $n$ is very small.

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Robert M. Guralnick; John Shareshian; Contributor-R. Stafford
Editore: American Mathematical Society (2007)
ISBN 10: 0821839926 ISBN 13: 9780821839928
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Descrizione libro American Mathematical Society, 2007. Paperback. Condizione libro: New. Brand new. We distribute directly for the publisher. The authors consider indecomposable degree $n$ covers of Riemann surfaces with monodromy group an alternating or symmetric group of degree $d$. They show that if the cover has five or more branch points then the genus grows rapidly with $n$ unless either $d = n$ or the curves have genus zero, there are precisely five branch points and $n =d(d-1)/2$.Similarly, if there is a totally ramified point, then without restriction on the number of branch points the genus grows rapidly with $n$ unless either $d=n$ or the curves have genus zero and $n=d(d-1)/2$. One consequence of these results is that if $f:X \rightarrow \mathbb{P}^1$ is indecomposable of degree $n$ with $X$ the generic Riemann surface of genus $g \ge 4$, then the monodromy group is $S_n$ or $A_n$ (and both can occur for $n$ sufficiently large).The authors also show if that if $f(x)$ is an indecomposable rational function of degree $n$ branched at $9$ or more points, then its monodromy group is $A_n$ or $S_n$. Finally, they answer a question of Elkies by showing that the curve parameterizing extensions of a number field given by an irreducible trinomial with Galois group $H$ has large genus unless $H=A_n$ or $S_n$ or $n$ is very small. Codice libro della libreria 1005260193

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Robert Guralnick, John Shareshian
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Descrizione libro American Mathematical Society, United States, 2007. Paperback. Condizione libro: New. Illustrated edition. Language: English . Brand New Book. The authors consider indecomposable degree $n$ covers of Riemann surfaces with monodromy group an alternating or symmetric group of degree $d$. They show that if the cover has five or more branch points then the genus grows rapidly with $n$ unless either $d = n$ or the curves have genus zero, there are precisely five branch points and $n =d(d-1)/2$. Similarly, if there is a totally ramified point, then without restriction on the number of branch points the genus grows rapidly with $n$ unless either $d=n$ or the curves have genus zero and $n=d(d-1)/2$. One consequence of these results is that if $f:X rightarrow mathbb{P 1$ is indecomposable of degree $n$ with $X$ the generic Riemann surface of genus $g ge 4$, then the monodromy group is $S n$ or $A n$ (and both can occur for $n$ sufficiently large). The authors also show if that if $f(x)$ is an indecomposable rational function of degree $n$ branched at $9$ or more points, then its monodromy group is $A n$ or $S n$.Finally, they answer a question of Elkies by showing that the curve parameterizing extensions of a number field given by an irreducible trinomial with Galois group $H$ has large genus unless $H=A n$ or $S n$ or $n$ is very small. Codice libro della libreria AAN9780821839928

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Robert Guralnick, John Shareshian
Editore: American Mathematical Society, United States (2007)
ISBN 10: 0821839926 ISBN 13: 9780821839928
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Descrizione libro American Mathematical Society, United States, 2007. Paperback. Condizione libro: New. Illustrated edition. Language: English . Brand New Book. The authors consider indecomposable degree $n$ covers of Riemann surfaces with monodromy group an alternating or symmetric group of degree $d$. They show that if the cover has five or more branch points then the genus grows rapidly with $n$ unless either $d = n$ or the curves have genus zero, there are precisely five branch points and $n =d(d-1)/2$. Similarly, if there is a totally ramified point, then without restriction on the number of branch points the genus grows rapidly with $n$ unless either $d=n$ or the curves have genus zero and $n=d(d-1)/2$. One consequence of these results is that if $f:X rightarrow mathbb{P 1$ is indecomposable of degree $n$ with $X$ the generic Riemann surface of genus $g ge 4$, then the monodromy group is $S n$ or $A n$ (and both can occur for $n$ sufficiently large). The authors also show if that if $f(x)$ is an indecomposable rational function of degree $n$ branched at $9$ or more points, then its monodromy group is $A n$ or $S n$.Finally, they answer a question of Elkies by showing that the curve parameterizing extensions of a number field given by an irreducible trinomial with Galois group $H$ has large genus unless $H=A n$ or $S n$ or $n$ is very small. Codice libro della libreria AAN9780821839928

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Descrizione libro American Mathematical Society, 2007. PAP. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria CE-9780821839928

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Robert Guralnick, John Shareshian
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Descrizione libro American Mathematical Society. Paperback. Condizione libro: new. BRAND NEW, Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces: Generic Covers and Covers with Many Branch Points - with an Appendix by R. Guralnick and R. Stafford: v. 1: Generic Covers and Covers with Many Branch Points - With an Appendix by R. Guralnick and R. Stafford (Illustrated edition), Robert Guralnick, John Shareshian, The authors consider indecomposable degree $n$ covers of Riemann surfaces with monodromy group an alternating or symmetric group of degree $d$. They show that if the cover has five or more branch points then the genus grows rapidly with $n$ unless either $d = n$ or the curves have genus zero, there are precisely five branch points and $n =d(d-1)/2$. Similarly, if there is a totally ramified point, then without restriction on the number of branch points the genus grows rapidly with $n$ unless either $d=n$ or the curves have genus zero and $n=d(d-1)/2$. One consequence of these results is that if $f:X \rightarrow \mathbb{P 1$ is indecomposable of degree $n$ with $X$ the generic Riemann surface of genus $g \ge 4$, then the monodromy group is $S n$ or $A n$ (and both can occur for $n$ sufficiently large). The authors also show if that if $f(x)$ is an indecomposable rational function of degree $n$ branched at $9$ or more points, then its monodromy group is $A n$ or $S n$.Finally, they answer a question of Elkies by showing that the curve parameterizing extensions of a number field given by an irreducible trinomial with Galois group $H$ has large genus unless $H=A n$ or $S n$ or $n$ is very small. Codice libro della libreria B9780821839928

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Descrizione libro Amer Mathematical Society, 2007. Paperback. Condizione libro: New. Codice libro della libreria DADAX0821839926

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Descrizione libro Amer Mathematical Society, 2007. Paperback. Condizione libro: New. book. Codice libro della libreria 0821839926

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Descrizione libro Amer Mathematical Society, 2007. Paperback. Condizione libro: Brand New. illustrated edition edition. 128 pages. 9.92x6.85x0.31 inches. In Stock. Codice libro della libreria __0821839926

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Descrizione libro Condizione libro: New. Depending on your location, this item may ship from the US or UK. Codice libro della libreria 97808218399280000000

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Descrizione libro Condizione libro: Brand New. Book Condition: Brand New. Codice libro della libreria 97808218399281.0

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