This volume is dedicated to the memory of the Russian mathematician D. A. Gudkov. It contains papers written by his friends, students, and collaborators and is devoted mainly to the areas where D. A. Gudkov made important contributions. The main topic is the topology of real algebraic varieties. Several papers include new results on the topology of real plane algebraic curves (the Hilbert 16th problem).

Readership

Graduate students and researchers interested in algebraic geometry and algebraic topology.

Table of Contents

• G. M. Polotovskii -- Dmitrii Andreevich Gudkov
• E. I. Gordon -- Recollection of D. A. Gudkov
• V. I. Arnold -- Remarks on the enumeration of plane curves
• A. Borobia and V. F. Mazurovskii -- On diagrams of configurations of 7 skew lines of \(\mathbb{R}^3\)
• B. Chevallier -- Smoothing isolated singularities on real algebraic surfaces
• A. I. Degtyarev -- Quadratic transformations \(\mathbb{R}P^2\to\mathbb{R}P^2\)
• P. M. Gilmer -- Real algebraic curves and link cobordism. II
• V. V. Goryunov -- Morsifications of rational functions
• I. V. Itenberg and E. I. Shustin -- Real algebraic curves with real cusps
• V. M. Kharlamov and I. V. Itenberg -- Towards the maximal number of components of a nonsingular surface of degree 5 in \(\mathbb{R}P^3\)
• Sergei I. Khashin and V. F. Mazurovskii -- Stable equivalence of real projective configurations
• A. Korchagin -- Smoothing of 6-fold singular points and constructions of 9th degree \(M\)-curves
• M. S. Kushelman -- Automaton model of relations between two countries
• T. V. Kuzmenko and G. M. Polotovskii -- Classification of curves of degree 6 decomposing into a product of \(M\)-curves in general position
• S. M. Natanzon -- Spinors and differentials of real algebraic curves
• V. V. Nikulin -- On the topological classification of real Enriques surfaces. I
• E. I. Shustin -- Critical points of real polynomials, subdivisions of Newton polyhedra and topology of real algebraic hypersurfaces
• G. A. Utkin -- On a nonlinear boundary value problem of mathematical physics
• O. Viro -- Generic immersions of the circle to surfaces and the complex topology of real algebraic curves
• V. I. Zvonilov -- Stratified spaces of real algebraic curves of bidegree \((m,1)\) and \((m,2)\) on a hyperboloid