Yang, Qilin Remarks on projective algebraic fiber spaces over curves. (English) Zbl 1099.14004 Commun. Algebra 34, No. 9, 3467-3474 (2006). 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 (\(n>4\)) PDFBibTeX XMLCite \textit{Q. Yang}, Commun. Algebra 34, No. 9, 3467--3474 (2006; Zbl 1099.14004) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.