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: 886

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9780821839928: 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: 886

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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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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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
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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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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 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 M. Guralnick, John Shareshian, R. Stafford (Contributor)
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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 2007. Paperback. Condizione libro: New. Illustrated edition. 8mm. Paperback. Considers indecomposable degree $n$ covers of Riemann surfaces with monodromy group an alternating or symmetric group of degree $d$. The authors show that if the cover has fi.Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. 128 pages. 0.266. Codice libro della libreria 9780821839928

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