A view on extending morphisms from ample divisors

The philosophy that ``a projective manifold is more special than any of its smooth hyperplane sections" was one of the classical principles of projective geometry. Lefschetz type results and related vanishing theorems were among the typically used techniques. We shall survey most of the problems, results and conjectures in this area, using the modern setting of ample divisors, and (some aspects of) Mori theory.Comment: To Appear in: Interactions of Classical and Numerical Algebraic Geometry, ed. by A. Bates, G. Besana and S. Di Rocco, Contemporary Mathematics, American Mathematical Societ

An Algebraic Approach to Hough Transforms

The main purpose of this paper is to lay the foundations of a general theory which encompasses the features of the classical Hough transform and extend them to general algebraic objects such as affine schemes. The main motivation comes from problems of detection of special shapes in medical and astronomical images. The classical Hough transform has been used mainly to detect simple curves such as lines and circles. We generalize this notion using reduced Groebner bases of flat families of affine schemes. To this end we introduce and develop the theory of Hough regularity. The theory is highly effective and we give some examples computed with CoCoA

Alternative approaches to Long Term Care financing. Distributive implications and sustainability for Italy.

In the last decade, many countries have adopted tax schemes specifically aimed at financing programs for Long Term Care (LTC). These mechanisms have important distributional implications both within and across generations. Given the process of demographic ageing, the issue of inter and intra-generational fairness is deeply linked with the problem of the long-term financial equilibrium of an LTC fund. In this paper we first compare, on a microdata sample of the Italian population, the distributive effects (both on current income and across generations) of six alternative approaches to finance an LTC scheme. In particular, we consider a hypothetical LTC scheme (with a size equivalent to that of the German one) to be introduced in Italy and analyse the distributive implications of some tax options, taken from the financing mechanisms implemented or under discussion in Germany, Luxembourg, Japan and Italy.In the second part of the paper we move from a static to a dynamic perspective: we study the long-term sustainability of an hypothetical Pay as You Go (Payg) LTC scheme operating in Italy (that is, assuming the Italian projected demographic trends) under scenarios that consider alternative indexation rules, growth rates of GNP, future incidence of disability among age groups.long term care; distributive effects; tax-benefit model; intertemporal sustainability; trust fund

Corrigendum for "Almost vanishing polynomials and an application to the Hough transform"

In this note we correct a technical error occurred in [M. Torrente and M.C. Beltrametti, "Almost vanishing polynomials and an application to the Hough transform", J. Algebra Appl. 13(8), (2014)]. This affects the bounds given in that paper, even though the structure and the logic of all proofs remain fully unchanged.Comment: 30 page

Manifolds covered by lines and extremal rays

Let $X$ be a smooth complex projective variety and let H \in \pic(X) be an ample line bundle. Assume that $X$ is covered by rational curves with degree one with respect to $H$ and with anticanonical degree greater than or equal to $(\dim X -1)/2$. We prove that there is a covering family of such curves whose numerical class spans an extremal ray in the cone of curves \cone(X).Comment: Major revision, to appear in Canadian Mathematical Bulleti