Deformations of canonical double covers

In this paper we show that if X is a smooth variety of general type of dimension m≥2 for which its canonical map induces a double cover onto Y, where Y is the projective space, a smooth quadric hypersurface or a smooth projective bundle over P1, embedded by a complete linear series, then the general deformation of the canonical morphism of X is again canonical and induces a double cover. The second part of the article proves the non-existence of canonical double structures on the rational varieties above mentioned. Our results have consequences for the moduli of varieties of general type of arbitrary dimension, since they show that infinitely many moduli spaces of higher dimensional varieties of general type have an entire “hyperelliptic” component. This is in sharp contrast with the case of curves or surfaces of lower Kodaira dimension.

E-polynomial of SL(2,C)-character varieties of complex curves of genus 3.

We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a complex curve of genus g = 3 into SL(2, C), and also of the moduli space of twisted representations. The case of genus g = 1, 2 has already been done in [12]. We follow the geometric technique introduced in [12], based on stratifying the space of representations, and on the analysis of the behaviour of the E-polynomial under fibrations.

Rational choice, social identity, and beliefs about oneself

Social identity poses one of the most important challenges to rational choice theory, but rational choice theorists do not hold a common position regarding identity. On one hand, externalist rational choice ignores the concept of identity or reduces it to revealed preferences. On the other hand, internalist rational choice considers identity as a key concept in explaining social action because it permits expressive motivations to be included in the models. However, internalist theorists tend to reduce identity to desire—the desire of a person to express his or her social being. From an internalist point of view, that is, from a viewpoint in which not only desires but also beliefs play a key role in social explanations as mental entities, this article rejects externalist reductionism and proposes a redefinition of social identity as a net of beliefs about oneself, beliefs that are indexical, robust, and socially shaped.