TY - CHAP
T1 - Equisingular families of projective curves
AU - Greuel, Gert Martin
AU - Lossen, Christoph
AU - Shustin, Eugenii
PY - 2006
Y1 - 2006
N2 - Summary: In this survey, we report on progress concerning families of projective curves with fixed number and fixed (topological or analytic) types of singularities. We are, in particular, interested in numerical, universal and asymptotically proper sufficient conditions to guarantee the nonemptyness, T-smoothness and irreducibility of the variety of all projective curves with prescribed singularities in a fixed linear system. We also discuss the analogous problem for hypersurfaces of arbitrary dimension with isolated singularities, and we close with a section on open problems and conjectures.
AB - Summary: In this survey, we report on progress concerning families of projective curves with fixed number and fixed (topological or analytic) types of singularities. We are, in particular, interested in numerical, universal and asymptotically proper sufficient conditions to guarantee the nonemptyness, T-smoothness and irreducibility of the variety of all projective curves with prescribed singularities in a fixed linear system. We also discuss the analogous problem for hypersurfaces of arbitrary dimension with isolated singularities, and we close with a section on open problems and conjectures.
UR - http://www.scopus.com/inward/record.url?scp=84892227156&partnerID=8YFLogxK
U2 - 10.1007/3-540-35480-8_5
DO - 10.1007/3-540-35480-8_5
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AN - SCOPUS:84892227156
SN - 3540354794
SN - 9783540354796
SP - 171
EP - 209
BT - Global Aspects of Complex Geometry
PB - Springer Berlin Heidelberg
ER -