Real Algebraic Surfaces

Abstract

These are the notes for my lectures at the Trento summer school held September 1997. The aim of the lectures is to provide an introduction to real algebraic surfaces using the minimal model program. This leads to a fairly complete understanding of real rational surfaces and to a complete topological classification of real Del Pezzo surfaces. Almost all the results are contained in the works of Comessatti and Silhol.

LATEX2e, 27 pages

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• Welschinger invariants of toric Del Pezzo surfaces with non-standard real structures
• Cylinders in weak del Pezzo fibrations
• Moduli of real pointed quartic curves
• Rationality of real conic bundles with quartic discriminant curve
• Real singular Del Pezzo surfaces and 3-folds fibred by rational curves, II
• Minimal degree rational curves on real surfaces
• Twenty-Seven Questions about the Cubic Surface
• A remark on Gromov-Witten-Welschinger invariants of $\mathbb{C}{P}^3\#{\overline{\mathbb{C}P}}^3$
• Real Rational Surfaces Are Quasi-Simple