How Long to Read Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I
By Robert M. Guralnick
How Long Does it Take to Read Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I?
It takes the average reader 2 hours and 12 minutes to read Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I by Robert M. Guralnick
Assuming a reading speed of 250 words per minute. Learn more
Description
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.
How long is Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I?
Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I by Robert M. Guralnick is 128 pages long, and a total of 33,024 words.
This makes it 43% the length of the average book. It also has 40% more words than the average book.
How Long Does it Take to Read Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I Aloud?
The average oral reading speed is 183 words per minute. This means it takes 3 hours to read Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I aloud.
What Reading Level is Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I?
Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I is suitable for students ages 10 and up.
Note that there may be other factors that effect this rating besides length that are not factored in on this page. This may include things like complex language or sensitive topics not suitable for students of certain ages.
When deciding what to show young students always use your best judgement and consult a professional.
Where Can I Buy Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I?
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