A Geometric Parametrization for the Virtual Euler Characteristics of the Moduli Spaces of Real and Complex Algebraic Curves

F eb 1 99 9 A geometric parametrization for the virtual Euler characteristics of the moduli spaces of real and complex algebraic curves ∗

Moduli spaces of surfaces and real structures

We give infinite series of groups Γ and of compact complex surfaces of general type S with fundamental group Γ such that 1) any surface S′ with the same Euler number as S, and fundamental group Γ, is diffeomorphic to S 2) the moduli space of S consists of exactly two connected components, exchanged by complex conjugation. Whence, i) on the one hand we give simple counter-examples to the DEF = D...

The equivariant Euler characteristic of moduli spaces of curves.

We give a formula for the Sn-equivariant Euler characteristics of the moduli spaces Mg,n of genus g curves with n marked points.

Geometry of Obstructed Equisingular Families of Algebraic Curves and Hypersurfaces

One of the main achievements of the algebraic geometry of the 20th century was to realize that it is fruitful not only to study algebraic varieties by themselves but also in families. That means that one should consider the space classifying all varieties with given properties. These spaces are called moduli spaces. The advantage of algebraic geometry is that many times those spaces are themsel...

On the Sn-equivariant Euler characteristic of moduli spaces of hyperelliptic curves

The generating function for Sn-equivariant Euler characteristics of moduli spaces of pointed hyperelliptic curves for any genus g ≥ 2 is calculated. This answer generalizes the known ones for genera 2 and 3 and answers obtained by J. Bergstrom for any genus and n ≤ 7 points.