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On certain remarkable curves of genus five. (English) Zbl 1057.14036

Here the author shows the existence of smooth genus five curves having exactly \(24\) Weierstrass points, which constitute the set of fixed points of \(3\) different elliptic involution, and proves that all such curves are bielliptic double covers of Fermat’s quartic. To construct the example he uses the projective geometry of elliptic normal quartics in \(\mathbb P^3\), i.e. the geometry of the smooth complete intersections of two quadric surfaces.

MSC:

14H45 Special algebraic curves and curves of low genus
14H50 Plane and space curves
14H55 Riemann surfaces; Weierstrass points; gap sequences
14N05 Projective techniques in algebraic geometry
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References:

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