We construct three new families of fibrations π : S → B where S is an algebraic complex surface and B a curve that violate Xiao’s conjecture relating the relative irregularity and the genus of the general fiber. The fibers of π are certain étale cyclic covers of hyperelliptic curves that give coverings of P 1 with dihedral monodromy. As an application, we also show the existence of big and nef effective divisors in the Brill–Noether range.

Dihedral monodromy and Xiao fibrations

ALBANO, Alberto;
2016-01-01

Abstract

We construct three new families of fibrations π : S → B where S is an algebraic complex surface and B a curve that violate Xiao’s conjecture relating the relative irregularity and the genus of the general fiber. The fibers of π are certain étale cyclic covers of hyperelliptic curves that give coverings of P 1 with dihedral monodromy. As an application, we also show the existence of big and nef effective divisors in the Brill–Noether range.
2016
195
4
1255
1268
http://arxiv.org/abs/1406.6308
Fibrations · Irregular surfaces · Prym varieties
Albano, Alberto; Pirola, Gian Pietro
File in questo prodotto:
File Dimensione Formato  
1406.6308v3.pdf

Accesso aperto

Descrizione: Articolo completo
Tipo di file: POSTPRINT (VERSIONE FINALE DELL’AUTORE)
Dimensione 187.58 kB
Formato Adobe PDF
187.58 kB Adobe PDF Visualizza/Apri
Albano-Pirola2016_Article_DihedralMonodromyAndXiaoFibrat.pdf

Accesso riservato

Tipo di file: PDF EDITORIALE
Dimensione 318.15 kB
Formato Adobe PDF
318.15 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

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/2318/1553936
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 8
  • ???jsp.display-item.citation.isi??? 7
social impact