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August 2020 On the Bielliptic and Bihyperelliptic Loci
Paola Frediani, Paola Porru
Michigan Math. J. 69(3): 571-600 (August 2020). DOI: 10.1307/mmj/1596700820

Abstract

We study some particular loci inside the moduli space M g , 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 A g if g 4 (whereas it is for g = 3 , see [18]) and that the bihyperelliptic locus is not totally geodesic in A g if g 3 g ' . 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.

Citation

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Paola Frediani. Paola Porru. "On the Bielliptic and Bihyperelliptic Loci." Michigan Math. J. 69 (3) 571 - 600, August 2020. https://doi.org/10.1307/mmj/1596700820

Information

Received: 16 July 2018; Revised: 17 August 2019; Published: August 2020
First available in Project Euclid: 6 August 2020

MathSciNet: MR4132605
Digital Object Identifier: 10.1307/mmj/1596700820

Subjects:
Primary: 14G35, 14H15, 14H40

Rights: Copyright © 2020 The University of Michigan

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Vol.69 • No. 3 • August 2020
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