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Topology of Real Algebraic Varieties
, 1998 In the first section, we prove some combinatorial topological properties of real algebraic sets; the simplest and most important of these properties is the fact that, for every semi-algebraic triangulation of a bounded algebraic set of dimension d and every (d - 1)-simplex σ of such a triangulation, the number of d-simplices of the triangulation having
Bochnak Jacek +2 more
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Topology of real algebraic varieties and related topics
, 1996 Dmitrii Andreevich Gudkov by G. M. Polotovskii Recollection of D. A. Gudkov by E. I. Gordon Remarks on the enumeration of plane curves by V. I. Arnold On diagrams of configurations of 7 skew lines of $\mathbb{R}^3$ by A. Borobia and V. F. Mazurovskii Smoothing isolated singularities on real algebraic surfaces by B. Chevallier Quadratic transformations $
Viro, Oleg Ya +3 more
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THE TOPOLOGY OF REAL PROJECTIVE ALGEBRAIC VARIETIES
Russian Mathematical Surveys, 1974 This article is a survey of the results on Hilbert's 16th problem from 1876 to the present. 1. HARNACK'S THEOREM. The number of branches of a non-singular curve of order m in RP2 does not exceed 1/2(m – 1)(m – 2) + 1. Harnack's method for constructing curves with the greatest number of branches (M-curves).
D A Gudkov
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Topology of real algebraic varieties and tropical homology
Singularities — Kagoshima 2017, 2020Ilia Itenberg
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Springer Monographs in Mathematics, 2020 This book gives a systematic presentation of real algebraic varieties. Real algebraic varieties are ubiquitous. They are the first objects encountered when learning of coordinates, then equations, but the systematic study of these objects, however ...
Frédéric Mangolte
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Gyroscopic stabilization of degenerate equilibria and the topology of real algebraic varieties
Doklady Mathematics, 2008exaly +2 more sources
The topology of two-dimensional real algebraic varieties
Annali di Matematica Pura ed Applicata, 1981E noto che ogni spazio analitico reale e localmente omeomorfo al cono su un poliedro con caratteristica di Eulero-Poincare pari. Si dimostra che questa condizione e anche sufficiente affinche un poliedro (compatto) di dimensione due P sia omeomorfo ad una varieta algebrica reale affine P.
Benedetti, R., Dedo, M.
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Progress in the topology of real algebraic varieties over the last six years
Russian Mathematical Surveys, 1986This is an extended version of the author's report to the Warsaw Congress [Proc. Int. Congr. Math., Warszawa 1983, Vol. 1, 603-619 (1984; Zbl 0571.14012)]. It is devoted to a circle of problems popularized by Hilbert in his 16-th problem from his famous talk at the Paris (1900) congress.
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