Trends in Singularities (Trends in Mathematics) - Hardcover

 
9783764367046: Trends in Singularities (Trends in Mathematics)
Hardcover
ISBN 10: 3764367040 ISBN 13: 9783764367046
Verlag: Birkhäuser, 2002

Inhaltsangabe

The collection of papers in this volume represents recent advances in the under­ standing of the geometry and topology of singularities. The book covers a broad range of topics which are in the focus of contemporary singularity theory. Its idea emerged during two Singularities workshops held at the University of Lille (USTL) in 1999 and 2000. Due to the breadth of singularity theory, a single volume can hardly give the complete picture of today’s progress. Nevertheless, this collection of papers provides a good snapshot of what is the state of affairs in the field, at the turn of the century. Several papers deal with global aspects of singularity theory. Classification of fam­ ilies of plane curves with prescribed singularities were among the first problems in algebraic geometry. Classification of plane cubics was known to Newton and classification of quartics was achieved by Klein at the end of the 19th century. The problem of classification of curves of higher degrees was addressed in numerous works after that. In the paper by Artal, Carmona and Cogolludo, the authors de­ scribe irreducible sextic curves having a singular point of type An (n > 15) and a large (Le. , :::: 18) sum of Milnor numbers of other singularities. They have discov­ ered many interesting properties of these families. In particular they have found new examples of so-called Zariski pairs, i. e.

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Reseña del editor

The collection of papers in this volume represents recent advances in the under­ standing of the geometry and topology of singularities. The book covers a broad range of topics which are in the focus of contemporary singularity theory. Its idea emerged during two Singularities workshops held at the University of Lille (USTL) in 1999 and 2000. Due to the breadth of singularity theory, a single volume can hardly give the complete picture of today's progress. Nevertheless, this collection of papers provides a good snapshot of what is the state of affairs in the field, at the turn of the century. Several papers deal with global aspects of singularity theory. Classification of fam­ ilies of plane curves with prescribed singularities were among the first problems in algebraic geometry. Classification of plane cubics was known to Newton and classification of quartics was achieved by Klein at the end of the 19th century. The problem of classification of curves of higher degrees was addressed in numerous works after that. In the paper by Artal, Carmona and Cogolludo, the authors de­ scribe irreducible sextic curves having a singular point of type An (n > 15) and a large (Le. , :::: 18) sum of Milnor numbers of other singularities. They have discov­ ered many interesting properties of these families. In particular they have found new examples of so-called Zariski pairs, i. e.

Reseña del editor

The collection of papers in this volume represents recent advances in the geometry and topology of singularities. Written by well-known specialists, the articles cover a broad range of topics that provide a focus for ongoing research and investigation. The contributions discuss local as well as global aspects, endowing the reader with an overview on the present state of the art.
The volume is intended for a large audience in pure and applied mathematics, including researchers and graduate students working in algebraic geometry, singularity theory, topology and related fields. The reader will find up-to-date information on a wide variety of contemporary problems involving singularities.

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Verlag
Birkhäuser
Erscheinungsdatum
2002
Sprache
Englisch
ISBN 10 
3764367040
ISBN 13 
9783764367046
Einband
Tapa dura
Anzahl der Seiten
260
Herausgeber
Libgober Anatoly, Tibăr Mihai
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar

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