2004/01/30 by Romain Bondil, Bondil, Romain
Computer Science · Mathematics · #14B07 #32S25 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary - 32S15 #Secondary - 14H20 #math.AG #msc:14B07 #msc:14H20 #msc:32S15 #msc:32S25
paper · pdf · doi:10.48550/arxiv.math/0401434
Janvier 2004
arxiv created 2004/01/30 · openalex publication_date 2004/01/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the polar curves \PSO arising from generic projections of a germ (S,0) of complex surface singularity onto \C2. Taking (S,0) to be a minimal singularity of normal surface (i.e. a rational singularity with reduced tangent cone), we give the δ-invariant of these polar curves, as well as the equisingularity-type of their generic plane projections, which are also the discriminants of generic projections of (S,0). These two (equisingularity)-data for \PSO are described in term, on the one side of the geometry of the tangent cone of (S,0) and on the other side of the limit-trees introduced by T. de Jong and D. van Straten for the deformation theory of these minimal singularities. These trees give a combinatorial device for the description of the polar curve which makes it much clearer than in our previous Note on the subject. This previous work mainly relied on a result of M. Spivakovsky. Here we give a geometrical proof via deformations (on the tangent cone, and what we call Scott deformations) and blow-ups, although we need Spivakovsky's result at some point, extracting some other consequences of it along the way.