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Plane quartics with Jacobians isomorphic to a hyperelliptic Jacobian. (English) Zbl 0974.14021
According to Torelli’s theorem any smooth projective curve over an algebraically closed field is determined by its polarized Jacobian variety. G. Humbert in [Journ. de Math. (5) 6, 279-386 (1900; JFM 31.0455.04)] gave the first example of two non-isomorphic curves (of genus 2) with the same unpolarized Jacobian. Later many more such examples have been given. The present paper constructs for any positive integer $$n$$ distinct smooth plane quartics and one hyperelliptic curve of genus 3 such that all $$n+1$$ of these curves have isomorphic unpolarized Jacobian variety. The construction produces explicit equations for curves over $$\mathbb{C}$$ whose Jacobians are isomorphic as unpolarized abelian varieties.

##### MSC:
 14H40 Jacobians, Prym varieties 14H45 Special algebraic curves and curves of low genus
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##### References:
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