Title | Trends in Singularities [electronic resource] / edited by Anatoly Libgober, Mihai Tibฤ{131}r |
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Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2002 |

Connect to | http://dx.doi.org/10.1007/978-3-0348-8161-6 |

Descript | IX, 246 p. online resource |

SUMMARY

The collection of papers in this volume represents recent advances in the underยญ 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 famยญ 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 deยญ 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 discovยญ ered many interesting properties of these families. In particular they have found new examples of so-called Zariski pairs, i. e

CONTENT

On Sextic Curves with Big Milnor Number -- Rรฉsolution des Singularitรฉs de Surfaces par ร{137}clatements Normalisรฉs -- Sectional Singularities and Geometry of Families of Planar Quadratic Forms -- On the Cohomology of Fibres of Polynomial Maps -- Generic Torelli for Semiquasihomogeneous Singularities -- Eigenvalues for the Monodromy of the Milnor Fibers of Arrangements -- Fundamental Group of Sextics of Torus Type -- Universal Abelian Covers of Surface Singularities -- On Real Singularities with a Milnor Fibration -- Braid Monodromy Type Invariants of Surfaces and 4-Manifolds -- Singularities and Topology of Meromorphic Functions

Mathematics
Algebraic geometry
Mathematics
Algebraic Geometry