论文信息 - Gluing of singular and critical points

Gluing of singular and critical points

Abstract We suggest an approach to construction of algebraic hypersurfaces with given collection of singular points and polynomials with given collection of critical points. The approach is based on the Viro method of gluing polynomials and on the geometry of equisingular and equicritical strata in spaces of polynomials. As application we construct cuspidal plane curves of small degrees and real polynomials in two variables with given numbers of degenerate and non-degenerate critical points.

Eugenii Shustin | E. Shustin

[1] Friedrich Hirzebruch,et al. Singularities of algebraic surfaces and characteristic numbers , 1986 .

[2] Oscar Zariski,et al. Studies in Equisingularity II. Equisingularity in Codimension 1 (and Characteristic Zero) , 1965 .

[3] Oleg Viro,et al. Gluing of plane real algebraic curves and constructions of curves of degrees 6 and 7 , 1984 .

[4] A. G. Kouchnirenko. Polyèdres de Newton et nombres de Milnor , 1976 .

[5] V. K. Patodi. Geometry and Analysis: Papers Dedicated to the Memory of V.K. Patodi , 1982 .

[6] V. Arnold. On some problems in singularity theory , 1981 .

[7] Alan H. Durfee,et al. Counting Critical Points of Real Polynomials in Two Variables , 1993 .

[8] D A Gudkov,et al. THE TOPOLOGY OF REAL PROJECTIVE ALGEBRAIC VARIETIES , 1974 .

[9] Oscar Zariski,et al. Studies in Equisingularity I Equivalent Singularities of Plane Algebroid Curves , 1965 .

[10] O. Lyashko. Decomposition of simple singularities of functions , 1976 .

[11] Oscar Zariski,et al. Studies in Equisingularity III: Saturation of Local Rings and Equisingularity , 1968 .

[12] I. M. Gelʹfand,et al. Discriminants, Resultants, and Multidimensional Determinants , 1994 .

[13] E. Shustin. Real plane algebraic curves with prescribed singularities , 1993 .

[14] G. Greuel,et al. Families of varieties with prescribed singularities , 1989 .