Canonical Surfaces and Hypersurfaces in Abelian Varieties

The present work deals with the canonical map of smooth, compact complex surfaces of general type in a polarization of type $(1, 2, 2)$ on an abelian threefold. A natural and classical question to ask is whether the canonical system of such surfaces is in general very ample. In this work, we provide a positive answer to this question. We describe the behavior of the canonical map of a smooth surface S in a polarization of type $(1, 2, 2)$ on an abelian threefold A in some special situations, and we prove by deformation arguments that the canonical map is a holomorphic embedding when A and S are sufficiently general. It follows in particular a proof of the existence of canonical irregular spaces in $\mathbb{P}^5$ with numerical invariants $p_g = 6$, $q = 3$ and $K^2 = 24$.Comment: 31 page

Canonical Surfaces an Hypersurfaces in Abelian Varieties

The present work deals with the canonical map of smooth, compact complex surfaces of general type, which induce a polarization of type (1,2,2) on an abelian threefold. The aim of the present study is to provide a geometric description of the canonical map of a smooth surface S of type (1,2,2) in an abelian threefold A in some special situations, and to prove that, when A and S are sufficiently general, the canonical system of S is very ample. It follows, in particular, a proof of the existence of canonical irregular surfaces in P5 with numerical invariants $p_g = 6$, $q = 3$ and $K^2 = 24$. This thesis is organized as follows: The first chapter deals with the basic theore- tical results concerning ample divisors on abelian varieties and their canonical map, which can be analytically represented in terms of theta functions. In this context, the example of surfaces in a polarization of type $(1, 1, 2)$ on an Abelian threefold, is of particular importance: the behavior of the canonical map of the pullback of a principal polarization by a degree 2 isogeny has been described by F. Catanese by investigating the canonical image and its defining projective equations by means of homological methods. In the last section of the first chapter, we treat in detail these results, as well as the connection with the analytical representation of the canonical map presented at the beginning of the same chapter. The polarization types $(1, 2, 2)$ and $(1, 1, 4)$ cannot be distinguished by considering only the numeric invariants of the ample surfaces in the respective linear systems. In the second chapter, we study the unramified bidouble covers of a smooth non-hyperelliptic curve of genus $3$, and we characterize the unramified bidouble covers of a general Jacobian $3$-folds, which carry a polarization of type $(1, 2, 2)$. In the third and last chapter of this thesis we investigate the behaviour of the canonical map of a general smooth surface in a polarization of type $(1,2,2)$ on an abelian threefold $A$, which is an etale quotient of a product of a $(2, 2)$-polarized abelian surface with a $(2)$-polarized elliptic curve. With this analysis and with some monodromy arguments, we prove the main result of this thesis, which states that the canonical system of a general smooth surface $S$ of type $(1, 2, 2)$ in a general abelian threefold $A$ yields a holomorphic embedding in $\mathbb{P}^5$

A Real-time Energy-Saving Mechanism in Internet of Vehicles Systems

Emerging technologies, such as self-driving cars and 5G communications, are raising new mobility and transportation possibilities in smart and sustainable cities, bringing to a new echo-system often referred to as Internet of Vehicles (IoV). In order to efficiently operate, an IoV system should take into account more stringent requirements with respect to traditional IoT systems, e.g., ultra-broadband connections, high-speed mobility, high-energy efficiency and requires efficient real-time algorithms. This paper proposes an energy and communication driven model for IoV scenarios, where roadside units (RSUs) need to be frequently assigned and re-assigned to the operating vehicles. The problem has been formulated as an Uncapacitated Facility Location Problem (UFLP) for jointly solving the RSU-to-vehicle allocation problem while managing the RSUs switch-on and -off processes. Differently from traditional UFLP approaches, based on static solutions, we propose here a fast-heuristic approach, based on a dynamic multi-period time scale mapping: the proposed algorithm is able to efficiently manage in real-time the RSUs, selecting at each period those to be activated and those to be switched off. The resulting methodology is tested against a set of benchmark instances, which allows us to illustrate its potential. Results, in terms of overall cost –mapping both energy consumption and transmission delays–, number of active RSUs, and convergence speed, are compared with static approaches, showing the effectiveness of the proposed dynamic solution. It is noticeable a gain of up to 11% in terms of overall cost with respect to the static approaches, with a moderate additional delay for finding the solution, around 0.8 s, while the overall number of RSUs to be switched on is sensibly reduced up to a fraction of 15% of the overall number of deployed RSUs, in the most convenient scenario

A Real-Time Energy-Saving Mechanism in Internet of Vehicles Systems

[EN] Emerging technologies, such as self-driving cars and 5G communications, are raising new mobility and transportation possibilities in smart and sustainable cities, bringing to a new echo-system often referred to as Internet of Vehicles (IoV). In order to efficiently operate, an IoV system should take into account more stringent requirements with respect to traditional IoT systems, e.g., ultra-broadband connections, high-speed mobility, high-energy efficiency and requires efficient real-time algorithms. This paper proposes an energy and communication driven model for IoV scenarios, where roadside units (RSUs) need to be frequently assigned and re-assigned to the operating vehicles. The problem has been formulated as an Uncapacitated Facility Location Problem (UFLP) for jointly solving the RSU-to-vehicle allocation problem while managing the RSUs switch-on and -off processes. Differently from traditional UFLP approaches, based on static solutions, we propose here a fast-heuristic approach, based on a dynamic multi-period time scale mapping: the proposed algorithm is able to efficiently manage in real-time the RSUs, selecting at each period those to be activated and those to be switched off. The resulting methodology is tested against a set of benchmark instances, which allows us to illustrate its potential. Results, in terms of overall cost-mapping both energy consumption and transmission delays-, number of active RSUs, and convergence speed, are compared with static approaches, showing the effectiveness of the proposed dynamic solution. It is noticeable a gain of up to 11% in terms of overall cost with respect to the static approaches, with a moderate additional delay for finding the solution, around 0.8 s, while the overall number of RSUs to be switched on is sensibly reduced up to a fraction of 15% of the overall number of deployed RSUs, in the most convenient scenario.The work of Luca Cesarano and Andrea Croce has been done during an abroad study period at Universitat Oberta de Catalunya, Spain, supported by Erasmus+ Study Programme of the European Union.Cesarano, L.; Croce, A.; Martins, LDC.; Tarchi, D.; Juan-Pérez, ÁA. (2021). A Real-Time Energy-Saving Mechanism in Internet of Vehicles Systems. IEEE Access. 9:157842-157858. https://doi.org/10.1109/ACCESS.2021.3130125157842157858

Studio e simulazione di algoritmi euristici real-time per scenari Internet of Vehicles

Le ultime tecnologie del Cloud Computing, del 5G e dell’IoT permettono la nascita di nuove possibilità nell’ambito dei trasporti e della mobilità delle Smart City. Questi nuovi sistemi richiedono algoritmi molto efficienti che riescano, in real-time, a gestire un gran numero di dispositivi. Questo lavoro analizza il Multi-Period Internet of Vehicles Problem (MPIoVP), nel quale delle Road-side unit (RSU) devono essere assegnate a dei veicoli in movimento frequentemente: i processi di allocazione delle risorse devono essere veloci ed efficienti. Per risolvere l'MPIoVP è stato sviluppato un algoritmo agile. La metodologia risultante è messa alla prova contro un set di istanze benchmark al fine di mostrare il suo potenziale

Alla riscoperta delle politiche industriali

La tesi affronta il tema delle politiche industriali, che sono tornate a sollevare l'interesse dell'opinione pubblica dopo lo scoppio della crisi economico-finanziaria nel 2008. L'obiettivo principale di questo elaborato è definire e specificare il tema della politica industriale e individuare i punti di forza e di debolezza dell'intervento dello stato in economia. Il primo capitolo ripropone e approfondisce il confronto tra la visione funzionale, secondo cui lo Stato deve concentrarsi sulla fornitura di servizi, e la visione selettiva, secondo cui lo Stato deve favorire settori o imprese particolari. Il secondo capitolo ripercorre le tappe fondamentali del processo di sviluppo economico dell'Italia degli ultimi sessant'anni in modo da approfondire i fattori che hanno ostacolato la crescita e classificare gli strumenti della politica industriale di tipo funzionale. Il terzo capitolo mostra altri esempi di politica industriale: Unione Europea, Regno Unito, Stati Uniti d'America, Giappone, Corea del Sud e Cina. Per ogni paese ripercorro la storia e descrivo gli strumenti di politica industriale, a volte nascosti sotto il mantello della "mano invisibile", a volte esplicitamente previsti dai piani quinquennali

Canonical Surfaces and Hypersurfaces in in Abelian Varieties

The present work deals with the canonical map of smooth, compact complex surfaces of general type, which induce a polarization of type (1,2,2) on an abelian threefold. The aim of the present study is to provide a geometric description of the canonical map of a smooth surface S of type (1,2,2) in an abelian threefold A in some special situations, and to prove that, when A and S are sufficiently general, the canonical system of S is very ample. It follows, in particular, a proof of the existence of canonical irregular surfaces in P5 with numerical invariants pg = 6, q = 3 and K^2 = 24. This thesis is organized as follows: The first chapter deals with the basic theoretical results concerning ample divisors on abelian varieties and their canonical map, which can be analytically represented in terms of theta functions (see proposition 1.1.1). In this context, the example of surfaces in a polarization of type (1,1,2) on an Abelian threefold, which has been studied in [14], is of particular importance: the behavior of the canonical map of the pullback of a principal polarization by a degree 2 isogeny has been described in [14] by investigating the canonical image and its defining projective equations by means of homological methods. In the last section of the first chapter, we treat in detail these results, as well as the connection with the analytical representation of the canonical map presented at the beginning of the same chapter. The polarization types (1,2,2) and (1,1,4) cannot be distinguished by considering only the numeric invariants of the ample surfaces in the respective linear systems. In the second chapter, we study the unramified bidouble covers of a smooth non-hyperelliptic curve of genus 3, and we characterize the unramified bidouble covers of a general Jacobian 3-folds, which carry a polarization of type (1,2,2). In the third and last chapter of this thesis we investigate the behaviour of the canonical map of a general smooth surface in a polarization of type (1,2,2) on an abelian threefold A, which is an etale quotient of a product of a (2,2)-polarized abelian surface with a (2)-polarized elliptic curve. With this analysis and with some monodromy arguments, we prove the main result of this thesis, which states that the canonical system of a general smooth surface S of type (1,2,2) in a general abelian threefold A yields a holomorphic embedding in P5