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

Reducibility for a class of weakly dispersive linear operators arising from the Degasperis Procesi equation

We prove reducibility of a class of quasi-periodically forced linear equations of the form $$\partial_tu-\partial_x\circ (1+a(\omega t, x))u+\mathcal{Q}(\omega t)u=0,\quad x\in\mathbb{T}:=\mathbb{R}/2\pi\mathbb{Z},$$ where $u=u(t,x)$, $a$ is a small, $C^{\infty}$ function, $\mathcal{Q}$ is a pseudo differential operator of order $-1$, provided that $\omega\in\mathbb{R}^{\nu}$ satisfies appropriate non-resonance conditions. Such PDEs arise by linearizing the Degasperis-Procesi (DP) equation at a small amplitude quasi-periodic function. Our work provides a first fundamental step in developing a KAM theory for perturbations of the DP equation on the circle. Following \cite{Airy}, our approach is based on two main points: first a reduction in orders based on an Egorov type theorem then a KAM diagonalization scheme. In both steps the key difficulites arise from the asymptotically linear dispersion law. In view of the application to the nonlinear context we prove sharp \emph{tame} bounds on the diagonalizing change of variables. We remark that the strategy and the techniques proposed are applicable for proving reducibility of more general classes of linear pseudo differential first order operators

New examples of Calabi-Yau threefolds and genus zero surfaces

We classify the subgroups of the automorphism group of the product of 4 projective lines admitting an invariant anticanonical smooth divisor on which the action is free. As a first application, we describe new examples of Calabi-Yau 3-folds with small Hodge numbers. In particular, the Picard number is 1 and the number of moduli is 5. Furthermore, the fundamental group is non-trivial. We also construct a new family of minimal surfaces of general type with geometric genus zero, K^2=3 and fundamental group of order 16. We show that this family dominates an irreducible component of dimension 4 of the moduli space of the surfaces of general type.Comment: 18 pages; v2: simplified some arguments in the last section, final version to appear on Communications in Contemporary Mathematic

AN IMPACT ASSESSMENT OF THE FUTURE CAP REFORM ON THE ITALIAN TOMATO SECTOR

The Health Check (HC) document traces the path for a new revision of the CAP. The communication content can be summarised in the following points: decoupling at regional and not at historical level, a more intensive modulation mechanism differentiated according to the total volume of subsidy received by the farm and a new implementation of the art. 69. The aim of this paper is to assess the effect of the HC on the farms producing fruits and vegetables in Italy, with a particular emphasis on the processed tomato production. The model based on the PMP approach simulates the regionalisation mechanism and the new modulation per brackets. The analysis carried out on a FADN sample of farms located in Emilia-Romagna region highlights as the HC new measures affect the farm economic performances but not the input allocation choice. The flat rate doesn’t produce perturbation in the relative convenience of the crops maintaining unchanged the degree of substitution among activities. Only when the CAP mechanism moves from a coupling scenario to a total decoupling one and in the case of a variation in price levels the modifications inside the production plan are evident.Future CAP reforms, Tomato sector, CAP assessment, Agricultural and Food Policy, Political Economy, Q10, Q18,

Fast Escape from Quantum Mazes in Integrated Photonics

Escaping from a complex maze, by exploring different paths with several decision-making branches in order to reach the exit, has always been a very challenging and fascinating task. Wave field and quantum objects may explore a complex structure in parallel by interference effects, but without necessarily leading to more efficient transport. Here, inspired by recent observations in biological energy transport phenomena, we demonstrate how a quantum walker can efficiently reach the output of a maze by partially suppressing the presence of interference. In particular, we show theoretically an unprecedented improvement in transport efficiency for increasing maze size with respect to purely quantum and classical approaches. In addition, we investigate experimentally these hybrid transport phenomena, by mapping the maze problem in an integrated waveguide array, probed by coherent light, hence successfully testing our theoretical results. These achievements may lead towards future bio-inspired photonics technologies for more efficient transport and computation.Comment: 13 pages, 10 figure

Brain imaging in Kufs disease type B. case reports

The clinical traits of Kufs disease (KD) type B (CLN13), an adult-onset neuronal ceroid lipofuscinosis (NCL), are well established according to the neurological features of the cases reported with mutations in CTSF. The neuroradiological characteristics of this uncommon disease have not yet been outlined