Michigan Mathematical Journal

On the Bielliptic and Bihyperelliptic Loci

Paola Frediani and Paola Porru

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We study some particular loci inside the moduli space Mg, namely the bielliptic locus (i.e. the locus of curves admitting a 2:1 cover over an elliptic curve E) and the bihyperelliptic locus (i.e. the locus of curves admitting a 2:1 cover over a hyperelliptic curve C', g(C')2). We show that the bielliptic locus is not a totally geodesic subvariety of Ag if g4 (whereas it is for g=3, see [18]) and that the bihyperelliptic locus is not totally geodesic in Ag if g3g'. We also give a lower bound for the rank of the second Gaussian map at the generic point of the bielliptic locus and an upper bound for this rank for every bielliptic curve.

Article information

Michigan Math. J., Advance publication (2020), 30 pages.

Received: 16 July 2018
Revised: 17 August 2019
First available in Project Euclid: 31 January 2020

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Primary: 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18] 14H15: Families, moduli (analytic) [See also 30F10, 32G15] 14H40: Jacobians, Prym varieties [See also 32G20]


Frediani, Paola; Porru, Paola. On the Bielliptic and Bihyperelliptic Loci. Michigan Math. J., advance publication, 31 January 2020. doi:10.1307/mmj/1580439627. https://projecteuclid.org/euclid.mmj/1580439627

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