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Results tagged with hyperelliptic-curves
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user 1310
7
votes
About the characteristic polynomial of Frobenius of the Jacobian of a genus 2 hyperelliptic ...
The equation for $\# J_C(\mathbb F_p)$ that you quote contains a typo: they must have meant that $\# J_C(\mathbb F_p) = \frac 1 2 \# C(\mathbb F_{p^2}) + \frac 1 2 \# C(\mathbb F_p)^2 - p$, which is c …
- 40.2k
4
votes
What is the value of this hyperelliptic Hodge-type integral?
You are right that it's equivalent to compute the degree of the forgetful map. The degree is $3!$, since it's the quotient by $S_3$ permuting the last three markings. If you divide by $S_4$ you get th …
- 40.2k
7
votes
Is it true that every mapping class in $\mathrm{Mod}(\Sigma_3)$ commutes with some hyperelli...
No. After the Nielsen realization theorem, this follows from the classification of automorphism groups of genus three Riemann surfaces, which can be found in many places. For example, the cyclic group …
- 40.2k