Numerical bounds of canonical varieties

We study lower bounds for the self-intersection of the canonical divisor of "canonical varieties" (i.e. varieties whose canonical linear system gives a birational map). We give some improvements for the known results in the case of surfaces and new bounds for the case of canonical threefolds.Comment: 23 page

Stability and singularities of relative hypersurfaces

We study relative hypersurfaces over curves, and prove an instability condition for the fibres. This gives an upper bound on the log canonical threshold of the relative hypersurface. We compare these results with the information that can be derived from Nakayama's Zariski decomposition of effective divisors on relative projective bundles.Comment: 26 pages, 1 figure, revised version with minor change

Slopes of trigonal fibred surfaces and of higher dimensional fibrations

We give lower bounds for the slope of higher dimensional fibrations over curves under conditions of GIT-semistability of the fibres, using a generalization of a method of Cornalba and Harris. With the same method we establish a sharp lower bound for the slope of trigonal fibrations of even genus and general Maroni invariant; in particular this result proves a conjecture due to Harris and Stankova-Frenkel.Comment: 11 page

Linear stability of projected canonical curves with applications to the slope of fibred surfaces

Let f :S\to B be a non locally trivial fibred surface. We prove a lower bound for the slope of f depending increasingly from the relative irregularity of f and the Clifford index of the general fibres.Comment: Latex, 19 pages, revised version; to appear in J. of Math. Soc. of Japa

Stability and singularities of relative hypersurfaces

We study relative hypersurfaces, and prove an instability condition for the fibres. This is the starting point for an investigation of the geometry of effective divisors on relative projective bundles.Preprin

Capitalization, Regulation and the Poor: Access to Basic Services in Bolivia

Privatization, Regulation, Utilities, Poverty

Capitalization and Privatization in Bolivia: An Aproximation to an Evaluation

The paper describes the privatization process in Bolivia, placing emphasis on the particularities of the capitalization mechanism that was used for this purpose, and the regulatory framework introduced as its essential complement. With this background, the paper then details the changes in the industrial organization and ownership patterns in the electricity, oil and gas, telecommunications, transportation, and water industries. The discussion then turns to these processes’ economic and social consequences. In the first case, the key issues are which agents benefited from the transfer of assets, and the effects on firm-level variables like investment, profitability, and transfers to the State. With regards to social outcomes, we focus on the effects on employees and consumers. For the first, interest centers on what happened to employment and wages in the sectors affected; for the second, what occurred to access and prices for privatized utilities, and to welfare more generally. This paper touches on all these issues, although in several cases a full treatment is not possible due to data limitations.Privatization; Regulation; Economic Impact