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Families of Curves in P and Zeuthen's Problem

Buch | Softcover

96 Seiten

1998
American Mathematical Society (Verlag)
978-0-8218-0648-7 (ISBN)

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Presents 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. This work offers a 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.

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.

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.

Erscheint lt. Verlag	30.1.1998
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Gewicht	227 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8218-0648-3 / 0821806483
ISBN-13	978-0-8218-0648-7 / 9780821806487
Zustand	Neuware