Classification of normal quartic surfaces with irrational singularities. (English) Zbl 1068.14044

Ishii, Yuji; Nakayama, Noboru

J. Math. Soc. Japan 56, No. 3, 941-965 (2004).

Normal quartic surfaces in \(\mathbb P^3\) with irrational singularities are classified by determining their minimal desingularization. Such a surface is determined by its minimal desingularization \(M\), the pullback \(D\) of a generic hyperplane section and a non-zero effective anti-canonical divisor \(E\) on the desingularization. Geometric constructions of all possible triplets \((M,D,E)\) are given.

Reviewer: Gerhard Pfister (Kaiserslautern)

MSC:

14J25	Special surfaces
14J26	Rational and ruled surfaces
14J70	Hypersurfaces and algebraic geometry
14E30	Minimal model program (Mori theory, extremal rays)

Keywords:

ruled surface; extremal ray