Memoirs of the American Mathematical Society 1997; 96 pp; softcover Volume: 130 ISBN10: 0821806483 ISBN13: 9780821806487 List Price: US$46 Individual Members: US$27.60 Institutional Members: US$36.80 Order Code: MEMO/130/617
 This book provides a negative solution to Zeuthen's problem, which was proposed as a prize problem in 1901 by the Royal Danish Academy of Arts and Sciences. The problem was to decide whether every irreducible family of smooth space curves admits limit curves which are stick figures, composed of lines meeting only two at a time. To solve the problem, the author makes a detailed study of curves on cubic surfaces in \({\mathbb P}^3\) and their possible degenerations as the cubic surface specializes to a quadric plus a plane or the union of three planes. Readership Graduate students and research mathematicians interested in algebraic geometry. Table of Contents  Introduction
 Preliminaries
 Families of quadric surfaces
 Degenerations of cubic surfaces
 Standard form for certain deformations
 Local Picard group of some normal hypersurface singularities
 Solution of Zeuthen's problem
