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A Gudkov Certain theorems on curves of order m
points in general position and algebraic curves
A Gudkov Properties of rough spaces of sixth order curves with k singular
6 other sections not shown
algebraic curves algebraic surface algebraic variety analytic curve assertions are true Assume Bertini's theorem branch of F broken line coefficients components curve DF(x curve F curve H G curve H(t curve of category cusp denoted equation exists a curve exterior F x H following assertions fourth order surface G R2 genus Hence homeomorphic impossible interior ovaloids interior ovals irreducible curve isolated points isotopic Lemma Let F G linearly independent neighborhood node nonsingular Obviously ordinary double point ordinary point passing pencil point a0 point of osculation points d(F points in common points of intersection points z9 principal ovaloid property s3 real points real singular points rebifurcation F regular neighborhood satisfying shown on Figure shrinking singular unicursal curve sixth order curves statement straight line sufficiently small surface F surface of type system of points tangent plane tendrils triple point type in R2