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On moduli of real curves. (English) Zbl 0655.14011
Sémin. géométrie algébrique réelle, Paris 1986, Tome 2, Publ. Math. Univ. Paris VII 24, 85-95 (1986).
[For the entire collection see Zbl 0623.00004.]
The moduli space $$\bar M^ g$$ of isomorphism classes of stable complex algebraic curves of genus g is known to be a projective variety. The subspace $$\bar M^ g({\mathbb{R}})\subset \bar M^ g$$ of those curves definable by real polynomials is called the moduli space of real algebraic curves of genus g. It is shown that the space $$\bar M^ g({\mathbb{R}})$$ is connected. This contrasts with the situation for $$M^ g({\mathbb{R}})$$, the moduli space of smooth complex algebraic curves of genus g defined over the real numbers. This space is not connected.
Reviewer: N.Schwartz

##### MSC:
 14Pxx Real algebraic and real-analytic geometry 14H15 Families, moduli of curves (analytic) 32G15 Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables)