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manuscripta mathematica

, Volume 95, Issue 3, pp 273–287 | Cite as

Irregularity of certain algebraic fiber spaces

  • Jin-Xing Cai

Abstract:

Let X, Y be smooth complex projective varieties, and \(\) be a fiber space whose general fiber is a curve of genus g. Denote by q f the relative irregularity of f. It is proved that \(\), if f is not generically trivial; moreover, if either a) f is non-constant and the general fiber is either hyperelliptic or bielliptic or b) q(Y)= 0, then \(\), and the bound is best possible.

A classification of fiber surfaces of genus 3 with q f = 2 is also given in this note.

Mathematics Subject Classification (1991): 14J40 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jin-Xing Cai
    • 1
  1. 1.Institute of Mathematics, Peking University, Beijing 100871, P. R. China.¶e-mail: caijx@sxx0.math.pku.edu.cnCN

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