Asymptotic base loci on singular varieties

We prove that the non-nef locus and the restricted base locus of a pseudoeffective divisor coincide on KLT pairs. We also extend to KLT pairs F. Russo's characterization of nef and abundant divisors by means of asymptotic multiplier ideals.Comment: Improved exposition. To appear in "Math. Z.

Restricted volumes of effective divisors

We study the restricted volume of effective divisors, its properties and the relationship with the related notion of reduced volume, defined via multiplier ideals, and with the asymptotic intersection number. We build upon the fundamental work of Lazarsfeld and Mustata relating the restricted volume of big divisors to the volume of the associated Okounkov body. We extend their constructions and results to the case of effective divisors, recovering some results of Kaveh and Khovanskii, proving a Fujita-type approximation in this larger setting and studying the restricted volume function. In order to relate the reduced volume and the asymptotic intersection number we investigate a boundedness property of asymptotic multiplier ideals and prove it holds, for instance, for finitely generated divisors. In this way we obtain also a complete picture for the canonical divisor of an arbitrary smooth projective variety and for nef divisors on varieties of dimension at most 3.Comment: 32 page

Pluricanonical systems for 3-folds and 4-folds of general type

We explicitly find lower bounds on the volume of threefolds and fourfolds of general type in order to have nonvanishing of pluricanonical systems and birationality of pluricanonical maps. In the case of threefolds of large volume, we also give necessary and sufficient conditions for the fourth canonical map to be birational.Comment: 25 pages. Minor corrections and improved exposition. To appear in Mathematical Proceedings of the Cambridge Philosophical Societ

Evaluation of vegetation post-fire resilience in the Alpine region using descriptors derived from MODIS spectral index time series

In this study a method based on the analysis of MODerate-resolution Imaging Spectroradiometer (MODIS) time series is proposed to estimate the post-fire resilience of mountain vegetation (broadleaf forest and prairies) in the Italian Alps. Resilience is defined herewith as the ability of a dynamical system to counteract disturbances. It can be quantified by the amount of time the disturbed system takes to resume, in statistical terms, an ecological functionality comparable with its undisturbed behavior. Satellite images of the Normalized Difference Vegetation Index (NDVI) and of the Enhanced Vegetation Index (EVI) with spatial resolution of 250m and temporal resolution of 16 days in the 2000-2012 time period were used. Wildfire affected areas in the Lombardy region between the years 2000 and 2010 were analysed. Only large fires (affected area >40ha) were selected. For each burned area, an undisturbed adjacent control site was located. Data pre-processing consisted in the smoothing of MODIS time series for noise removal and then a double logistic function was fitted. Land surface phenology descriptors (proxies for growing season start/end/length and green biomass) were extracted in order to characterize the time evolution of the vegetation. Descriptors from a burned area were compared to those extracted from the respective control site by means of the one-way analysis of variance. According to the number of subsequent years which exhibit statistically meaningful difference between burned and control site, five classes of resilience were identified and a set of thematic maps was created for each descriptor. The same method was applied to all 84 aggregated events and to events aggregated by main land cover. EVI index results more sensitive to fire impact than NDVI index. Analysis shows that fire causes both a reduction of the biomass and a variation in the phenology of the Alpine vegetation. Results suggest an average ecosystem resilience of 6-7 years. Moreover, broadleaf forest and prairies show different post-fire behavior in terms of land surface phenology descriptors. In addition to the above analysis, another method is proposed, which derives from the qualitative theory of dynamical systems. The (time dependent) spectral index of a burned area over the period of one year was plotted against its counterpart from the control site. Yearly plots (or scattergrams) before and after the fire were obtained. Each plot is a sequence of points on the plane, which are the vertices of a generally self-intersecting polygonal chain. Some geometrical descriptors were obtained from the yearly chains of each fire. Principal Components Analysis (PCA) of geometrical descriptors was applied to a set of case studies and the obtained results provide a system dynamics interpretation of the natural process.JRC.H.3 - Forest Resources and Climat

Euler pseudoprimes for half of the bases

We prove that an odd number is an Euler pseudoprime for exactly one half of the admissible bases if and only if it is a special Carmichael number.Comment: 4 pages. To appear in Integer

Apolarity, Hessian and Macaulay polynomials

A result by Macaulay states that an Artinian graded Gorenstein ring R of socle dimension one and socle degree b can be realized as the apolar ring of a homogeneous polynomial f of degree b. If R is the Jacobian ring of a smooth hypersurface g=0, then b is just equal to the degree of the Hessian polynomial of g. In this paper we investigate the relationship between f and the Hessian polynomial of g.Comment: 12 pages. Improved exposition, minor correction

I.S.Mu.L.T. Achilles Tendon Ruptures Guidelines

This work provides easily accessible guidelines for the diagnosis, treatment and rehabilitation of Achilles tendon ruptures. These guidelines could be considered as recommendations for good clinical practice developed through a process of systematic review of the literature and expert opinion, to improve the quality of care for the individual patient and rationalize the use of resources. This work is divided into two sessions: 1) questions about hot topics; 2) answers to the questions following Evidence Based Medicine principles. Despite the frequency of the pathology andthe high level of satisfaction achieved in treatment of Achilles tendon ruptures, a global consensus is lacking. In fact, there is not a uniform treatment and rehabilitation protocol used for Achilles tendon ruptures

Indicatori comuni del PNRR e framework SDGs: una proposta di indicatore composito

The main component of the NextGeneration EU (NGEU) program is the Recovery and Resilience Facility (RRF), spanning an implementation period between 2021 and 2026. The RRF also includes a monitoring system: every six months, each country is required to send an update on the progress of the plan against 14 common indicators, measured on specific quantitative scales. The aim of this paper is to present the first empirical evidence on this system, while, at the same time, emphasizing the potential of its integration with the sustainable development framework (SDGs). We propose to develop a first linkage between the 14 common indicators and the SDGs which allows us to produce a composite index (SDGs-RRF) for France, Germany, Italy, and Spain for the period 2014-2021. Over this time, widespread improvements in the composite index across the four countries led to a partial reduction of the divergence. The proposed approach represents a first step towards a wider use of the SDGs for the assessment of the RRF, in line with their use in the European Semester documents prepared by the European Commission.Comment: 30 pages, in Italian, 10 figures, 13 table