The moduli space of real algebraic curves of genus 2. (Q1880006)

It is well-known that the connected components of the moduli space of real algebraic curves of a given genus \(g\) are determined by the number of real ovals \(k\leq g+1\) and the number, \(1\) or \(2\), of the connected components of the complement of real ovals in the complexification. The author describes all five connected components of the moduli space of real algebraic curves of genus \(2\), representing them by \(3\)-parameter families of plane quartic and quintic curves. Subsets, corresponding to curves with specific automorphism groups, are indicated in the above families.