Sakai, Fumio On polarized normal surfaces. (English) Zbl 0635.14016 Manuscr. Math. 59, 109-127 (1987). A polarized normal surface consists of a normal projective surface Y over \({\mathbb{C}}\) and an ample Cartier divisor H on Y. In Math. Ann. 275, 71-80 (1986; Zbl 0579.14017), M. Reid proves a structure theorem in the case where Y is a smooth and birationally ruled surface. In the present paper the author reformulates Reid’s theorem and proves a more general theorem where Y is normal with canonical divisor \(K_ Y\) not pseudoeffective. He also proves a classification theorem of extremal rational curves on normal surfaces with \(K_ Y\) not pseudoeffective which he uses in the proof of his main theorem. Reviewer: A.Papantonopoulou Cited in 2 Documents MSC: 14J10 Families, moduli, classification: algebraic theory 14C20 Divisors, linear systems, invertible sheaves 14H45 Special algebraic curves and curves of low genus 14J25 Special surfaces Keywords:polarized normal surface; canonical divisor; extremal rational curves Citations:Zbl 0588.14006; Zbl 0579.14017 PDFBibTeX XMLCite \textit{F. Sakai}, Manuscr. Math. 59, 109--127 (1987; Zbl 0635.14016) Full Text: DOI EuDML References: [1] BRENTON,L.:Some algebraicity criteria for singular surfaces. Invent. Math. 41, 129-147 (1977) · Zbl 0353.32031 · doi:10.1007/BF01418372 [2] IONESCU,P.:Generalized adjuction and applications. Math. Proc. Camb. Phil. Soc. 99, 457-472 (1986) · Zbl 0619.14004 · doi:10.1017/S0305004100064409 [3] KAWAMATA,Y.:The cone of curves of algebraic varieties. Ann. of Math. 119, 603-633 (1984) · Zbl 0544.14009 · doi:10.2307/2007087 [4] MORI,S.:Threefolds whose canonical bundles are not numerically effective. Ann. of Math. 116, 133-176 (1982) · Zbl 0557.14021 · doi:10.2307/2007050 [5] REID,M.:Surfaces of small degree. Math. Ann. 275, 71-80 (1986) · Zbl 0579.14017 · doi:10.1007/BF01458584 [6] SAKAI,F.:Weil divisors on normal surfaces. Duke Math. J. 51, 877-887 (1984) · Zbl 0602.14006 · doi:10.1215/S0012-7094-84-05138-X [7] SAKAI,F.:The structure of normal surfaces. Duke Math. J. 52, 627-648 (1985) · Zbl 0596.14025 · doi:10.1215/S0012-7094-85-05233-0 [8] SAKAI,F.:Ample Cartier divisors on normal surfaces. J. reine angew. Math. 366, 121-128 (1986) · Zbl 0582.14011 · doi:10.1515/crll.1986.366.121 [9] SAKAI,F.:Ruled fibrations on normal surfaces. To appear in J. Math. Soc. Japan · Zbl 0655.14014 [10] SOMMESE,A.:On the adunction theoretic structure of projective varieties. In: Lecture Notes in Math. 1194, pp. 175-213, Berlin-Heidelberg-New York: Springer, 1986 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.