Restricted simple Lie algebras and their infinitesimal deformations

In this expository paper, we first review the classification of the restricted simple Lie algebras in characteristic different from 2 and 3 and then we describe their infinitesimal deformations. We conclude by indicating some possible application to the deformations of simple finite group schemes.Comment: 11 pages, An Introduction to the classification of restricted simple Lie algebras and their deformation

Picard group of moduli of hyperelliptic curves

The main subject of this work is the difference between the coarse moduli space and the stack of hyperelliptic curves. We compute their Picard groups, giving explicit description of the generators. We get an application to the (non-)existence of a tautological family over the coarse moduli space.Comment: 13 pages. Section 2 has been shortened and the final appendix has been erased. Final version, to appear on Math. Zei

On the Picard group scheme of the moduli stack of stable pointed curves

The aim of the present paper is to study the (abstract) Picard group and the Picard group scheme of the moduli stack of stable pointed curves over an arbitrary scheme. As a byproduct, we compute the Picard groups of the moduli stack of stable or smooth pointed curves over a field of characteristic different from two.Comment: 36 pages. v2: added a new section on the first Chern class and the divisor class group of the coarse moduli spac

Asymptotically idempotent aggregation operators for trust management in multi-agent systems

The study of trust management in multi-agent system, especially distributed, has grown over the last years. Trust is a complex subject that has no general consensus in literature, but has emerged the importance of reasoning about it computationally. Reputation systems takes into consideration the history of an entity’s actions/behavior in order to compute trust, collecting and aggregating ratings from members in a community. In this scenario the aggregation problem becomes fundamental, in particular depending on the environment. In this paper we describe a technique based on a class of asymptotically idempotent aggregation operators, suitable particulary for distributed anonymous environments

The Quasi-Elastic Nuclear Response

We explore the nuclear responses at intermediate energies, particularly in the spin longitudinal and spin transverse isovector channels, within the continuum random phase approximation framework. We also employ an extension of the standard random phase approximation to account for the spreading width of the single particle states through the inclusion of a complex and energy-dependent nucleon self-energy. The nuclear responses are then used as the basic ingredient to calculate hadronic reactions in the Glauber theory framework. Here both one and two-step contributions to the multiple scattering series in the quasi-elastic peak region are taken into account. We find evidence for shell effects in the one-step response and a strong dependence on the momentum regime of the two-step contribution.Comment: 26 pages, REVTEX 2.1, 9 figures (Postscript, available from the Authors

On some modular contractions of the moduli space of stable pointed curves

The aim of this paper is to study some modular contractions of the moduli space of stable pointed curves. These new moduli spaces, which are modular compactifications of the moduli space of smooth pointed curves, are related with the minimal model program for the moduli space of stable pointed curves and have been introduced in a previous work of the authors. We interpret them as log canonical models of adjoints divisors and we then describe the Shokurov decomposition of a region of boundary divisors on the moduli space of stable pointed curves.Comment: 30 pages, 1 figure. To appear on Algebra and Number Theor

On the birational geometry of the universal Picard variety

We compute the Kodaira dimension of the universal Picard variety P_{d,g} parameterizing line bundles of degree d on curves of genus g under the assumption that (d-g+1,2g-2)=1. We also give partial results for arbitrary degrees d and we investigate for which degrees the universal Picard varieties are birational.Comment: 34 pages, 1 figure, final version (to appear in IMRN