Counting hyperelliptic curves

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dc.creatorNart, Enric
dc.date2007-03-19
dc.date.accessioned2026-07-07T07:52:38Z
dc.date.available2026-07-07T07:52:38Z
dc.descriptionWe find a closed formula for the number $\operatorname{hyp}(g)$ of hyperelliptic curves of genus $g$ over a finite field $k=\mathbb{F}_q$ of odd characteristic. These numbers $\operatorname{hyp}(g)$ are expressed as a polynomial in $q$ with integer coefficients that depend on the set of divisors of $q-1$ and $q+1$. As a by-product we obtain a closed formula for the number of self-dual curves of genus $g$. A hyperelliptic curve is self-dual if it is $k$-isomorphic to its own hyperelliptic twist.
dc.identifierhttps://arxiv.org/abs/math/0703549
dc.identifierhttp://arxiv.org/abs/math/0703549
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125949
dc.subjectNumber Theory
dc.subjectAlgebraic Geometry
dc.titleCounting hyperelliptic curves
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