On polarized normal surfaces (Q1097322)

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), \textit{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.