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Remarks on projective algebraic fiber spaces over curves. (English) Zbl 1099.14004

Summary: Let \(f:X\to C\) be a fibration over a curve \(C\) with general fiber \(F\). Some numerical characteristics of \(h^i(\mathcal O_X)\) in terms of \(h^i(\mathcal O_F)\), the genus \(g(C)\) and the degree of direct image sheaves \(R^i f_*(\omega_{X/C})\) are given. If \(f\) is the derived fibration induced by the \(m\)-canonical map, further numerical characterizations of \(m\)-plurigenus of \(F\) are given.

MSC:

14D06 Fibrations, degenerations in algebraic geometry
14E05 Rational and birational maps
14N05 Projective techniques in algebraic geometry
14J40 \(n\)-folds (\(n>4\))
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References:

[1] DOI: 10.1081/AGB-100106775 · Zbl 1079.14519 · doi:10.1081/AGB-100106775
[2] DOI: 10.1017/S0305004198002734 · Zbl 0957.14027 · doi:10.1017/S0305004198002734
[3] DOI: 10.1007/b75857 · Zbl 0992.14001 · doi:10.1007/b75857
[4] DOI: 10.1007/BF01404756 · Zbl 0461.14004 · doi:10.1007/BF01404756
[5] DOI: 10.2307/1971390 · Zbl 0605.14014 · doi:10.2307/1971390
[6] DOI: 10.2969/jmsj/04440643 · Zbl 0783.14021 · doi:10.2969/jmsj/04440643
[7] DOI: 10.1007/BF01457229 · Zbl 0571.14019 · doi:10.1007/BF01457229
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