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, Volume 95, Issue 1, pp 273–287 | Cite as

Irregularity of certain algebraic fiber spaces

  • Jin-Xing Cai


LetX, Y be smooth complex projective varieties, andf: XY be a fiber space whose general fiber is a curve of genusg. Denote byq f the relative irregularity off. It is proved thatq f ≤5g+1 / 6, iff 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, thenq f g+1 / 2, and the bound is best possible.

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

Mathematics Subject Classification (1991)



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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Jin-Xing Cai
    • 1
  1. 1.Institute of MathematicsPeking UniversityBeijingP. R. China

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