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Results tagged with hyperelliptic-curves
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not deleted
user 40297
5
votes
Rational functions on hyperelliptic Riemann surface
Yes (the answer was given, then deleted, by Francesco Polizzi). If $D$ and $D'$ are the divisors of zeroes (resp. poles) of a rational function, the linear system $|D|$ has dimension $r\geq 1$ and is …
- 38k
6
votes
Accepted
Curves of higher genus
I am not sure whether this answers your question: it is a conjecture of Coleman that for a fixed genus $g$ sufficiently high, there should be only finitely many CM Jacobians of genus $g$. In fact Cole …
- 38k
1
vote
Accepted
Linear systems and 2-torsion shifts on hyperelliptic curves
This will never happen. The linear systems of degree $g+1$ on $C$ with
a base point are of the form $g^1_2+F$, with $F$ effective of degree $g-1$; in $J^{g+1}C$, they form a divisor $\Delta $ which …
- 38k
11
votes
Accepted
Non trivial family of hyperelliptic curves
If it was, $Y:=(X\times S)/(f\times g)$ would be isomorphic to $X\times F$. One way to see this is not the case is to look at 3-forms: $X\times F$ has no nonzero holomorphic 3-forms (because $H^0(F,\O …
- 38k