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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
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Trends in Singularities (Hardcover, 2002 ed.)
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Trends in Singularities (Hardcover, 2002 ed.)
Series: Trends in Mathematics
Expected to ship within 10 - 15 working days
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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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