Calabi–Yau threefolds and moduli of abelian surfaces I

We describe birational models and decide the rationality/unirationality of moduli spaces $\cal A$d (and $\cal A$levd) of (1, d)-polarized Abelian surfaces (with canonical level structure, respectively) for small values of d. The projective lines identified in the rational/unirational moduli spaces correspond to pencils of Abelian surfaces traced on nodal threefolds living naturally in the corresponding ambient projective spaces, and whose small resolutions are new Calabi–Yau threefolds with Euler characteristic zero

The moduli space of (111)-polarized abelian surfaces is unirational

We prove that the moduli space $\cal A$11lev of (1,11)-polarized Abelian surfaces with level structure of canonical type is birational to Klein's cubic hypersurface in P4. Therefore, $\cal A$11lev is unirational but not rational, and there are no Γ11-cusp forms of weight 3. The same methods also provide an easy proof of the rationality of $\cal A$9lev

Stochastic approximations and differential inclusions II: applications

We apply the theoretical results on "stochastic approximations and differential inclusions" developed in Benaim, Hofbauer and Sorin (2005) to several adaptive processes used in game theory including: classical and generalized approachability, no-regret potential procedures (Hart and Mas-Colell), smooth fictitious play (Fudenberg and Levine

The cc-map, Tits Satake subalgebras and the search for N=2\mathcal{N}=2 inflaton potentials

In this paper we address the general problem of including inflationary models exhibiting Starobinsky-like potentials into (symmetric) $\mathcal{N}=2$ supergravities. This is done by gauging suitable abelian isometries of the hypermultiplet sector and then truncating the resulting theory to a single scalar field. By using the characteristic properties of the global symmetry groups of the $\mathcal{N}=2$ supergravities we are able to make a general statement on the possible $\alpha$-attractor models which can obtained upon truncation. We find that in symmetric $\mathcal{N}=2$ models group theoretical constraints restrict the allowed values of the parameter $\alpha$ to be $\alpha=1,\,\frac{2}{3},\, \frac{1}{3}$. This confirms and generalizes results recently obtained in the literature. Our analysis heavily relies on the mathematical structure of symmetric $\mathcal{N}=2$ supergravities, in particular on the so called $c$-map connection between Quaternionic K\"ahler manifolds starting from Special K\"ahler ones. A general statement on the possible consistent truncations of the gauged models, leading to Starobinsky-like potentials, requires the essential help of Tits Satake universality classes. The paper is mathematically self-contained and aims at presenting the involved mathematical structures to a public not only of physicists but also of mathematicians. To this end the main mathematical structures and the general gauging procedure of $\mathcal{N}=2$ supergravities is reviewed in some detail.Comment: 101 pages, LaTeX sourc

The N=2 supersymmetric unconstrained matrix GNLS hierarchies

The generalization of the N=2 supersymmetric chiral matrix (k|n,m)--GNLS hierarchy (Lett. Math. Phys. 45 (1998) 63, solv-int/9711009) to the case when matrix entries are bosonic and fermionic unconstrained N=2 superfields is proposed. This is done by exhibiting the corresponding matrix Lax--pair representation in terms of N=2 unconstrained superfields. It is demonstrated that when matrix entries are chiral and antichiral N=2 superfields, it reproduces the N=2 chiral matrix (k|n,m)-GNLS hierarchy, while in the scalar case, k=1, it is equivalent to the N=2 supersymmetric multicomponent hierarchy (J. Phys. A29 (1996) 1281, hep-th/9510185). The simplest example --the N=2 unconstrained (1|1,0)--GNLS hierarchy-- and its reduction to the N=2 supersymmetric {\alpha}=1 KdV hierarchy are discussed in more detail, and its rich symmetry structure is uncovered.Comment: 11 pages, LaTex, misprints correcte

Family Abuse Against Minors

This study is a general analysis of data included in the statistics of the General Directorate of Romanian Penitentiaries with respect to violent crimes, sexual crimes and crimes related to deviations from social cohabitation rules in 2007. The study assesses, for this purpose the distribution, according to various indicators (sex, age, original environment, the relationship with the aggressor), of the victims of the abovementioned crimes, and also emphasizes the main risk factors which impact on, or cause, victimization rates

Suicide in Europe in the Context of the Global Economic Crisis

Starting from Durkheim's hypothesis according to which crisis periods cause a significant increase in the number of suicides, the author examines several variables associated with the recent economic crisis and the extent to which they influence suicide rates in Europe, including Romania. In this respect, an assessment is made of the findings of theoretical studies and empirical surveys conducted in several European countries, according to which the increase of unemployment rates, the decline of welfare standards and the deterioration of health conditions (including those related to mental health) are among the main factors associated with the increase of suicide rates in different countries