Real Kodaira surfaces

In this paper we give the topological classification of real primary Kodaira surfaces and we describe in detail the structure of the corresponding moduli space. One of the main tools is the orbifold fundamental group of a real variety. Our first result is that if $(S, \sigma)$ is a real primary Kodaira surface, then the differentiable type of the pair $(S,\sigma)$ is completely determined by the orbifold fundamental group exact sequence. This result allows us to determine all the possible topological types of $(S, \sigma)$. Finally, we show that once we fix the topological type of $(S, \sigma)$ corresponding to a real primary Kodaira surface, the corresponding moduli space is irreducible (and connected).Comment: 29 page

On the second gaussian map for curves on a K3 surface

By a theorem of Wahl, for canonically embedded curves which are hyperplane sections of K3 surfaces, the first gaussian map is not surjective. In this paper we prove that if C is a general hyperplane section of high genus (greater than 280) of a general polarized K3 surface, then the second gaussian map of C is surjective. The resulting bound for the genus g of a general curve with surjective second gaussian map is decreased to g >152.Comment: final version, to appear in Nagoya Mathematical Journa

Etale homotopy types of moduli stacks of algebraic curves with symmetries

Using the machinery of etale homotopy theory a' la Artin-Mazur we determine the etale homotopy types of moduli stacks over \bar{\Q} parametrizing families of algebraic curves of genus g greater than 1 endowed with an action of a finite group G of automorphisms, which comes with a fixed embedding in the mapping class group, such that in the associated complex analytic situation the action of G is precisely the differentiable action induced by this specified embedding of G in the mapping class group.Comment: 27 page

Deformation in the large of some complex manifolds, II

The compact complex manifolds considered in this article are principal torus bundles over a torus. We consider the Kodaira Spencer map of the complete Appell Humbert family (introduced by the first author in Part I) and are able to show that we obtain in this way a connected component of the space of complex structures each time that the base dimension is two, the fibre dimension is one, and a suitable topological condition is verified.Comment: 23 pages, to appear in the AMS Series 'Contemporary Mathematics',in the Proceedings of the 10th anniversary (2004) Conference for the Mathematics Institute at East China Normal Universit

Prym map and second gaussian map for Prym-canonical line bundles

We show that the second fundamental form of the Prym map lifts the second gaussian map of the Prym-canonical bundle. We prove, by degeneration to binary curves, that this gaussian map is surjective for the general point [C,A] of R_g for g > 19.Comment: Final version. To appear in Advances in Mathematic

Shimura varieties in the Torelli locus via Galois coverings

Given a family of Galois coverings of the projective line we give a simple sufficient condition ensuring that the closure of the image of the family via the period mapping is a special (or Shimura) subvariety in A_g. By a computer program we get the list of all families in genus up to 8 satisfying our condition. There is no family in genus 8, all of them are in genus at most 7. These examples are related to a conjecture of Oort. Among them we get the cyclic examples constructed by various authors (Shimura, Mostow, De Jong-Noot, Rohde, Moonen and others) and the abelian non-cyclic examples found by Moonen-Oort. We get 7 new non-abelian examples.Comment: Final version. To appear on Intenational Mathematics Research Notice

Re-imagining Participatory Design: Reflecting on the ASF-UK Change by Design Methodology

The thinking and practice of participatory design in processes of urban development and informal settlement upgrading has been associated with a variety of agendas and purposes. Sometimes it has been used as a mechanism of “inclusion” for a predefined vision and ideal of the city, and at other times it has been used as a means to expand the “collective power to reshape the processes of urbanization”. Similar discussions have taken place in debates around the links between democracy and design, in which design has sometimes been approached as a means of improving or enabling structures of governance and at other times of opening up new spaces for contestation and trajectories for social change

Monodromies of generic real algebraic functions

AbstractIn this paper we give a combinatorial description of the monodromies of real generic (non constant) holomorphic functions f:C→P1(C), where C is a compact connected Riemann surface of genus g. The monodromy of the branched covering of P1(C) given by such a function f can be described by means of a graph with labeled edges. In this paper we describe completly these graphs in the real generic case (i.e., when all the critical values of f have multiplicity one) and also in the case in which ∞ is the only non generic critical value. We are also able to compute the number of such graphs in the case in which the functions are real generic, of degree 3 and the genus varies. Finally we generalize a result obtained in the polynomial case together with F. Catanese, namely we prove that the number of connected components of the Hurwitz space of complex lemniscate generic algebraic functions (i.e., functions whose critical values have distinct absolute values) is equal to the number of monodromy graphs of real generic algebraic functions whose critical values are all real