Electronic ISBN:  9781470402068 
Product Code:  MEMO/130/617.E 
List Price:  $46.00 
MAA Member Price:  $41.40 
AMS Member Price:  $27.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 130; 1997; 96 ppMSC: Primary 14;
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.ReadershipGraduate students and research mathematicians interested in algebraic geometry.

Table of Contents

Chapters

0. Introduction

1. Preliminaries

2. Families of quadric surfaces

3. Degenerations of cubic surfaces

4. Standard form for certain deformations

5. Local Picard group of some normal hypersurface singularities

6. Solution of Zeuthen’s problem


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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.
Graduate students and research mathematicians interested in algebraic geometry.

Chapters

0. Introduction

1. Preliminaries

2. Families of quadric surfaces

3. Degenerations of cubic surfaces

4. Standard form for certain deformations

5. Local Picard group of some normal hypersurface singularities

6. Solution of Zeuthen’s problem