Prym Varieties of étale covers of hyperelliptic curves

• Herbert Lange ^[2] ; Angela Ortega ^[1]
  1. [1] Humboldt University of Berlin

     Humboldt University of Berlin

     Berlin, Stadt, Alemania

     
  2. [2] Universität Erlangen, Germany
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 18, Nº 2, 2018, págs. 467-482
• Idioma: inglés
• Enlaces
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• Resumen

  • It is well known that the Prym variety of an e´tale cyclic covering of a hyperelliptic curve is isogenous to the product of two Jacobians. Moreover, if the degree n of the covering is odd or congruent to 2 mod 4, then the canonical isogeny is an isomorphism. It is a natural question whether thisistrue for arbitrary degrees. We show that this is not the case by computing the degree of the isogeny for n a power of 2. Furthermore, we compute the degree of a closely related isogeny for arbitrary n.