Paola Frediani

Siegel metric and curvature of the moduli space of curves

We study the curvature of the moduli space Mg of curves of genus g with the Siegel metric induced by the period map j : Mg! Ag. We give an explicit formula for the holomorphic sectional curvature of Mg along a Schiffer variationP, for P a point on the curve X, in terms of the holomorphic sectional curvature of Ag and the second Gaussian map. Finally we extend the Kahler form of the Siegel metric as a closed current on M g and we determine its cohomology class as a multiple of �.

REAL HYPERELLIPTIC SURFACES AND THE ORBIFOLD FUNDAMENTAL GROUP

In this paper we finish the topological classification of real algebraic surfaces of Kodaira dimension zero and we make a step towards the Enriques classification of real algebraic surfaces, by describing in detail the structure of the moduli space of real hyperelliptic surfaces. Moreover, we point out the relevance in real geometry of the notion of the orbifold fundamental group of a real variety, and we discuss related questions on real varieties

On totally geodesic submanifolds in the Jacobian locus

(X, \sigma)

Hyperplane sections of abelian surfaces

whose underlying complex manifold

On the second Gaussian map for curves on a K3 surface

X

Monodromies of generic real algebraic functions

is a

Étale homotopy types of moduli stacks of polarised abelian schemes

K (\pi, 1)

A bound on the dimension of a totally geodesic submanifold in the Prym locus

. Our first result is that if

On the first Gaussian map for Prym-canonical line bundles

(S, \sigma)

Some results on the second Gaussian map for curves

is a real hyperelliptic surface, then the differentiable type of the pair