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- W1002809364 abstract "Let $e(E_1,ldots,E_r)$ be the minimum genus of a closed Riemann surface whose jacobian variety is isogenous to a product $E_1 times cdots times E_r times A$, where $A$ is a product of jacobian varietes and $E_{1},ldots, E_{r}$ are elliptic curves. Let $e(r)$ be the maximum of these values $e(E_1,ldots,E_r)$. If $r leq 3$, then it is known that $e(E_1,ldots,E_r)=r=e(r)$. We prove that (i) if $r geq 4$ is even, then $e(r) leq 1+2^{(r-2)/2}r$ and (ii) if $r geq 5$ is odd, then $e(r) leq 1+2^{(r-3)/2}(r-1)$. This is done by constructing explicit Riemann surfaces whose jacobian variety is isogenous to a product of any given $r$ elliptic curves with some others jacobian varieties. The construction also permits to obtain a $2$-dimensional family of Riemann surfaces of genus $g in {5,9}$ whose jacobian varieties are isogenous to the product of $g$ elliptic curves and also a $1$-dimensional family of Riemann surfaces of genus $13$ whose jacobian varieties are isogenous to the product of $13$ elliptic curves." @default.
- W1002809364 created "2016-06-24" @default.
- W1002809364 creator A5055194674 @default.
- W1002809364 date "2015-07-28" @default.
- W1002809364 modified "2023-09-27" @default.
- W1002809364 title "Elliptic factors on the jacobian variety of Riemann Surfaces" @default.
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