The generalized Mukai conjecture for symmetric varieties

We associate to any complete spherical variety $X$ a certain nonnegative rational number $\wp(X)$, which we conjecture to satisfy the inequality $\wp(X) \le \operatorname{dim} X - \operatorname{rank} X$ with equality holding if and only if $X$ is isomorphic to a toric variety. We show that, for spherical varieties, our conjecture implies the generalized Mukai conjecture on the pseudo-index of smooth Fano varieties due to Bonavero, Casagrande, Debarre, and Druel. We also deduce from our conjecture a smoothness criterion for spherical varieties. It follows from the work of Pasquier that our conjecture holds for horospherical varieties. We are able to prove our conjecture for symmetric varieties.Comment: 33 pages, 2 figures, 6 table

Gorenstein spherical Fano varieties

We obtain a combinatorial description of Gorenstein spherical Fano varieties in terms of certain polytopes, generalizing the combinatorial description of Gorenstein toric Fano varieties by reflexive polytopes and its extension to Gorenstein horospherical Fano varieties due to Pasquier. Using this description, we show that the rank of the Picard group of an arbitrary $d$-dimensional $\mathbb{Q}$-factorial Gorenstein spherical Fano variety is bounded by $2d$. This paper also contains an overview of the description of the natural representative of the anticanonical divisor class of a spherical variety due to Brion.Comment: 22 pages, 3 figure

Homogeneous spherical data of orbits in spherical embeddings

Let $G$ be a connected reductive complex algebraic group. Luna assigned to any spherical homogeneous space $G/H$ a combinatorial object called a homogeneous spherical datum. By a theorem of Losev, this object uniquely determines $G/H$ up to $G$-equivariant isomorphism. In this paper, we determine the homogeneous spherical datum of a $G$-orbit $X_0$ in a spherical embedding $G/H \hookrightarrow X$. As an application, we obtain a description of the colored fan associated to the spherical embedding $X_0 \hookrightarrow \bar{X_0}$.Comment: 14 pages, 1 tabl

The Manin-Peyre conjecture for smooth spherical Fano varieties of semisimple rank one

The Manin-Peyre conjecture is established for a class of smooth spherical Fano varieties of semisimple rank one. This includes all smooth spherical Fano threefolds of type T as well as some higher-dimensional smooth spherical Fano varieties.Comment: 75 page

A combinatorial smoothness criterion for spherical varieties

We suggest a combinatorial criterion for the smoothness of an arbitrary spherical variety using the classification of multiplicity-free spaces, generalizing an earlier result of Camus for spherical varieties of type $A$.Comment: 14 pages, 2 table

Assessment of the Effects of Autonomous Mowers on Plant Biodiversity in Urban Lawns

Gaining information on the impact of lawn management with autonomous mowers on the floristic composition is crucial to improve their plant biodiversity. In this study, an autonomous mower with a reduced mowing frequency and a more sporadic mowing management system with a ride-on rotary mower were compared in terms of the effect on three dicotyledonous species (Phyla nodiflora, Lotus corniculatus and Sulla coronaria) transplanted onto stands of Bermuda and Manila grass. Regardless of the management system, P. nodiflora achieved the best results in terms of survival for both lawns (74.92 and 58.57% in Manila and Bermuda grass, respectively). In Bermuda grass, a higher percentage of surviving individuals was observed for the ordinary mower management system (42.59%), rather than with the autonomous mower (9.10%), while no differences emerged on Manila grass. On both Manila and Bermuda grass, a higher average percentage of coverage for single individual was observed for the ordinary mower management system (1.60 and 0.37%, respectively) compared to the autonomous mower system (0.55 and 0.08%, respectively). P. nodiflora had a higher percentage of individuals with flowers with the ordinary management system rather than with autonomous mower system both on Manila (60.73% and 33.90%, respectively) and Bermuda grass (48.66 and 3.32%, respectively). Despite a lower impact on the planted species being observed for the ordinary mower management system, encouraging results were obtained with the autonomous mower, for instance regarding the percentage of surviving individuals for P. nodiflora (33.95%) and L. corniculatus (22.08%) on Bermuda grass and the percentage of individuals with flowers for the same two species (33.90 and 13.59%, respectively) on Manila grass. Furthermore, the autonomous mower management system’s primary energy consumption over the year was lower compared to that of the ordinary system both on Manila (200.4 and 614.97 kWh ha−1 year−1, respectively) and Bermuda grass (177.82 and 510.99 kWh ha−1 year−1, respectively)

L' efficacia degli incentivi agli investimenti in sicurezza.

Il quaderno fornisce un quadro assolutamente inedito sullo strumento degli Incentivi di Sostegno alle Imprese, i cosiddetti Bandi ISI, che sostengono le imprese che realizzano investimenti che migliorino le condizioni di sicurezza e di salute dei luoghi di lavoro. Idealmente la politica mira a un target di imprese caratterizzate da maggiore rischio, a causa della piccola dimensione o del tipo di lavorazione o ancora del settore produttivo, e fornisce un contributo a fondo perduto per realizzare investimenti che apportino una riduzione del rischio di infortunio o di quello di contrarre malattie professionali. Si tratta della prima volta in cui viene pubblicato un quadro completo del sistema di implementazione di questa politica gestita dall’Inail, quadro dotato di un ampio corredo di informazioni qualitative e quantitative. Questo è stato reso possibile per la piena collaborazione offerta dall’Istituto Nazionale per l’Assicurazione contro gli Infortuni sul Lavoro (Inail) che nel proprio Piano delle attività di ricerca 2016-2018 aveva già intrapreso un percorso di ricerca che aveva come obiettivo la valutazione della sostenibilità e dell’efficacia degli interventi di prevenzione