Irregularity of certain algebraic fiber spaces |
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Authors: | Jin-Xing Cai |
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Affiliation: | Institute of Mathematics, Peking University, Beijing 100871, P. R. China.?e-mail: caijx@sxx0.math.pku.edu.cn, CN
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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. Received: 19 March 1997 / Revised version: 29 October 1997 |
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Keywords: | Mathematics Subject Classification (1991): 14J40 |
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