We give a new example of a curve C algebraically, but not rationally, uniformized by radicals. This means that C has no map onto P1 with solvable Galois group, while there exists a curve C′ that maps onto C and has a finite morphism to P1 with solvable Galois group. We construct such a curve C of genus 9 in the second symmetric product of a general curve of genus 2. It is also an example of a genus 9 curve that does not satisfy condition S(4,2,9) of Abramovich and Harris.

A new curve algebraically but not rationally uniformized by radicals

SCHLESINGER, ENRICO ETTORE MARCELLO
2014-01-01

Abstract

We give a new example of a curve C algebraically, but not rationally, uniformized by radicals. This means that C has no map onto P1 with solvable Galois group, while there exists a curve C′ that maps onto C and has a finite morphism to P1 with solvable Galois group. We construct such a curve C of genus 9 in the second symmetric product of a general curve of genus 2. It is also an example of a genus 9 curve that does not satisfy condition S(4,2,9) of Abramovich and Harris.
File in questo prodotto:
File Dimensione Formato  
AJM 18-1-07-2.pdf

Accesso riservato

: Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione 149.99 kB
Formato Adobe PDF
149.99 kB Adobe PDF   Visualizza/Apri
AJM_11311-861404_Schlesinger.pdf

accesso aperto

: Pre-Print (o Pre-Refereeing)
Dimensione 159.71 kB
Formato Adobe PDF
159.71 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/861404
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact