Topological properties of real algebraic varieties: du côté de chez Rokhlin

Abstract

The survey gives an overview of the achievements in topology of real algebraic varieties in the direction initiated in the early 70th by V.I.Arnold and V.A.Rokhlin. We make an attempt to systematize the principal results in the subject. After an exposition of general tools and results, special attention is paid to surfaces and curves on surfaces.

References in corpus (1)

• On the Pontrjagin-Viro form

Cited by in corpus (19)

• On Real Structures of Rigid Surfaces
• Refined curve counting on complex surfaces
• Homology class of a Lagrangian Klein bottle
• On the number of components of a complete intersection of real quadrics
• Generalised Thurston-Bennequin invariants for real algebraic surface singularities
• Real loci in (log-) Calabi-Yau manifolds via Kato-Nakayama spaces of toric degenerations
• Euler characteristic and signature of real semi-stable degenerations
• Nombres de Betti des surfaces elliptiques réelles
• Real Kodaira surfaces
• Moduli of real pointed quartic curves
• Mirror Duality in a Joyce Manifold
• On wall-crossing invariance of certain sums of Welschinger numbers
• Classification of real rational knots of low degree in the 3-sphere
• The Expected Depth of Random Real Algebraic Plane Curves
• Shapes of surfaces that contain a great and a small circle through each point
• The real Mordell-Weil group of rational elliptic surfaces and real lines on del Pezzo surfaces of degree $K^2=1$
• Topological types of real regular jacobian elliptic surfaces
• Trigonal Morsifications on Hirzebruch Surfaces with an appendix by E. Shustin
• Estimates of Characteristic numbers of real algebraic varieties