In this article we investigate the algebra and geometry of dihedral covers of smooth algebraic varieties. To this aim we first describe the Weil divisors and the Picard group of divisorial sheaves on normal double covers. Then we provide a structure theorem for dihedral covers, that is, given a smooth variety Y, we describe the algebraic “building data” on Y which are equivalent to the existence of such covers π:X→Y. We introduce then two special very explicit classes of dihedral covers: the simple and the almost simple dihedral covers, and we determine their basic invariants. For the simple dihedral covers we also determine their natural deformations. In the last section we give an application to fundamental groups.

Dihedral Galois covers of algebraic varieties and the simple cases

PERRONI, FABIO
2017

Abstract

In this article we investigate the algebra and geometry of dihedral covers of smooth algebraic varieties. To this aim we first describe the Weil divisors and the Picard group of divisorial sheaves on normal double covers. Then we provide a structure theorem for dihedral covers, that is, given a smooth variety Y, we describe the algebraic “building data” on Y which are equivalent to the existence of such covers π:X→Y. We introduce then two special very explicit classes of dihedral covers: the simple and the almost simple dihedral covers, and we determine their basic invariants. For the simple dihedral covers we also determine their natural deformations. In the last section we give an application to fundamental groups.
Pubblicato
http://www.sciencedirect.com/science/article/pii/S0393044016302479
File in questo prodotto:
File Dimensione Formato  
perroni.pdf

non disponibili

Tipologia: Documento in Versione Editoriale
Licenza: Digital Rights Management non definito
Dimensione 560.11 kB
Formato Adobe PDF
560.11 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
2889628_perroni-PostPrint.pdf

accesso aperto

Descrizione: Post Print VQR3
Tipologia: Bozza finale post-referaggio (post-print)
Licenza: Digital Rights Management non definito
Dimensione 985.76 kB
Formato Adobe PDF
985.76 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/11368/2889628
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 4
social impact