Affine curves of degree 6 and smoothings of a non-degenerate sixth order singular point. (English. Russian original) Zbl 0679.14011

Math. USSR, Izv. 33, No. 3, 501-520 (1989); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 52, No. 6, 1181-1199 (1988).
The positions of projective curves with respect to a straight line are considered in \(RP^ 2\) instead of affine curves. The case when a straight line intersects a curve of degree \( 6\) in 6 points lying on the same oval is studied in detail. Let the family of curves \(F_ t(x,y)=0\), \(t\in [0,1]\), realize some smoothings (nonsingular perturbations) of an isolate nondegenerate singular point of multiplicity six of a curve \(F_ 0(x,y)=0\). It is proved that this smoothing is the image of some nonsingular affine curve of degree \( 6\) under a special homomorphism.
Reviewer: V.F.Ignatenko


14H20 Singularities of curves, local rings
14B07 Deformations of singularities
14N05 Projective techniques in algebraic geometry
14H45 Special algebraic curves and curves of low genus
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