A divisor on the moduli space of curves associated to the signature of fibered surfaces (with an appendix by Kazuhiro Konno)

Ashikaga, Tadashi; Yoshikawa, Ken-Ichi

doi:10.2969/aspm/05610001

VOL. 56 | 2009 A divisor on the moduli space of curves associated to the signature of fibered surfaces (with an appendix by Kazuhiro Konno)

Chapter Author(s) Tadashi Ashikaga, Ken-Ichi Yoshikawa

Editor(s) Jean-Paul Brasselet, Shihoko Ishii, Tatsuo Suwa, Michel Vaquie

Adv. Stud. Pure Math., 2009: 1-34 (2009) DOI: 10.2969/aspm/05610001

Abstract

In this note, we study the problem of localizing the signature of a fibered surface, i.e., a compact complex surface equipped with the structure of a fiber space over a compact Riemann surface. As applications, we give an estimate for the number of critical points and a formula for the Horikawa index for a certain class of fibered surfaces.