In this paper we investigate the numerical properties of relatively minimal isotrivial fibrations phi : X -> C, where X is a smooth, projective surface and C is a curve. In particular we prove that, if g(C) >= 1 and X is neither ruled nor isomorphic to a quasi-bundle, then K(X)(2) <= 8 chi(O(X)) - 2; this inequality is sharp and if equality holds then X is a minimal surface of general type whose canonical model has precisely two ordinary double points as singularities. Under the further assumption that K(X) is ample, we obtain K(X)(2) <= 8 chi(O(X)) - 5 and the inequality is also sharp. This improves previous results of Serrano and Tan.

Numerical properties of isotrivial fibrations

POLIZZI, Francesco
2010-01-01

Abstract

In this paper we investigate the numerical properties of relatively minimal isotrivial fibrations phi : X -> C, where X is a smooth, projective surface and C is a curve. In particular we prove that, if g(C) >= 1 and X is neither ruled nor isomorphic to a quasi-bundle, then K(X)(2) <= 8 chi(O(X)) - 2; this inequality is sharp and if equality holds then X is a minimal surface of general type whose canonical model has precisely two ordinary double points as singularities. Under the further assumption that K(X) is ample, we obtain K(X)(2) <= 8 chi(O(X)) - 5 and the inequality is also sharp. This improves previous results of Serrano and Tan.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

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/20.500.11770/157486
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 17
social impact