A single pdf file with the available part of the book.

• 1 Early Study of Real Algebraic Plane Curves   [pdf], [ps]
  • 1.1 Basic Definitions and Problems
  • 1.2 Digression: the Topology of Closed One-Dimensional Submanifolds of the Projective Plane
  • 1.3 Bézout's Prohibitions and the Harnack Inequality
  • 1.4 Curves of Degree $\le 5$
  • 1.5 The Classical Method of Constructing Nonsingular Plane Curves
  • 1.6 Harnack Curves
  • 1.7 Digression: the Space of Real Projective Plane Curves
  • 1.8 End of the Proof of Theorem 1.6.A
  • 1.9 Isotopy Types of Harnack M-Curves
  • 1.10 Hilbert Curves
  • 1.11 Analysis of the Results of the Constructions. Ragsdale
  • 1.12 Generalizations of Harnack's and Hilbert's Methods. Brusotti. Wiman
  • 1.13 The First Prohibitions not Obtained from Bézout's Theorem
  • Exercises
• 2 A Real Algebraic Curve from the Complex Point of View   [pdf], [ps]
  • 2.1 Complex Topological Characteristics of a Real Curve
  • 2.2 The First Examples
  • 2.3 Classical Small Perturbations from the Complex Point of View
  • 2.4 Further Examples
  • 2.5 Digression: Oriented Topological Plane Curves
  • 2.6 The Simplest Restrictions on a Complex Scheme
  • 2.7 Rokhlin's Complex Orientation Formula
  • 2.8 Complex Schemes of Degree $\le 5$
  • Exercises
• 3 The Topological Point of View on Prohibitions   [pdf], [ps]
  • 3.1 Flexible Curves
  • 3.2 The Most Elementary Prohibitions on Real Topology of a Flexible Curve
  • 3.3 A Survey of Prohibitions on the Real Schemes Which Come from Topology
  • 3.4 Survey of Prohibitions on the Complex Schemes Which Come From Topology
  • 3.5 Ideas of Some Proofs
  • 3.6 Flexible Curves of Degrees $\le 5$
  • 3.7 Sharpness of the Inequalities
  • 3.8 Prohibitions not Proven for Flexible Curves
• 4 The Comlexification of a Curve from a Real Viewpoint   [pdf], [ps]
  • 4.1 Curves with Maximal Nest Revised
  • 4.2 Fiedler's Alternation of Orientations
  • 4.3 Complex Orientations and Pencils of Lines. Alternative Approach
  • 4.4 Curves of Degree 7
• 5 Real Algebraic Spatial Surfaces   [pdf], [ps]
  • 5.1 Basic Definitions and Problems
  • 5.2 Digression: Topology of Closed Two-Dimensional Submanifolds of $\mathbb{R}P^3$
  • 5.3 Restrictions on Topology of Real Algebraic Surfaces
  • 5.4 Surfaces of Low Degree
• Bibliography
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