The main aim of this paper is to present an easy to use methodology for assessing the potential amount of electricity or thermal energy production in urban areas located in natural protected sites. The methodology is based on two different steps: a territorial analysis for the evaluation of solar radiation and usable surfaces for photovoltaic or solar thermal plant, and a plant analysis for highlighting those photovoltaic and solar thermal technologies which installation will not generate significant impacts in areas characterized by high environmental and landscaping value. The methodology was successfully applied in two case studies inside two different Italian natural protected areas. The obtained results were provided to local administrations and communities as a useful tool for sustainable energy planning.

Abstract:
We use a quite concrete and simple realization of $\slq$ involving finite difference operators. We interpret them as derivations (in the non-commutative sense) on a suitable graded algebra, which gives rise to the double of the projective line as the non commutative version of the standard homogeneous space.

Abstract:
We prove the following: (a) Let X be a smooth, codimension two subvariety of P6. If X lies on a hyperquintic or if deg(X)<74, then X is a complete intersection. (b) Let X be a smooth, subcanonical threefold in P5. If X lies on a hyperquartic, then X is a complete intersection.

Abstract:
For a projective variety $Z$ and for any integer $p$, define the $p$-th N\'eron-Severi group $NS_p(Z)$ of $Z$ as the image of the cycle map $A_{p}(Z)\to H_{2p}(Z; \mathbb{C})$. Now let $X\subset \Ps^{2m+1}$ ($m\geq 1$) be a projective variety of dimension $2m-1$, with isolated singularities, complete intersection of a smooth hypersurface of degree $k$, with a hypersurface of degree $n>max\{k, 2m+1\}$, and let $F$ be a general hypersurface of degree $n$ containing $X$. We prove that the natural map $NS_m(X)\to NS_m(F)$ is surjective, and that if $dim NS_m(F)=1$ then $dim NS_m(X)=1$. In particular $dim NS_m(X)=1$ if and only if $dim NS_m(F)=1$. When $X$ is a threefold (i.e. $m=2$) we deduce a new characterization for the factoriality of $X$, i.e. that $X$ is factorial if and only if $dim NS_2(F)=1$. This allows us to give examples of factorial threefolds, in some case with many singularities. During the proof of the announced results, we show that the quotient of the middle cohomology of $F$ by the cycle classes coming from $X$ is irreducible under the monodromy action induced by the hypersurfaces of degree $n$ containing $X$. As consequences we deduce a Noether-Lefschetz Theorem for a projective complete intersection with isolated singularities, and, also using a recent result on codimension two Hodge conjecture, in the case $X\subset \Ps^{5}$ is a threefold as before, we deduce that the general hypersurface $F$ of degree $n$ containing $X$ verifies Hodge conjecture.

Abstract:
Fix integers $r,d,s,\pi$ with $r\geq 4$, $d\gg s$, $r-1\leq s \leq 2r-4$, and $\pi\geq 0$. Refining classical results for the genus of a projective curve, we exhibit a sharp upper bound for the arithmetic genus $p_a(C)$ of an integral projective curve $C\subset {\mathbb{P}^r}$ of degree $d$, assuming that $C$ is not contained in any surface of degree $ \pi$. Next we discuss other types of bound for $p_a(C)$, involving conditions on the entire Hilbert polynomial of the integral surfaces on which $C$ may lie.

Abstract:
We define an adelic version of a CM curve which takes care of all the automorphisms and which is naturally equipped with an embedding into the adelic Heisenberg group. We embed into the adelic Heisenberg group the set of commensurability classes of arithmetic 1-dimensional K-lattices and define theta functions on it. We thus get an algebra of functions on the set of 1-dimensional K-lattices which is equipped with an action of the Heisenberg group and which exibits a nice behavior under complex automorphisms (Theorem 7.12).

Abstract:
We describe how to obtain the imprimitivity bimodules of the noncommutative torus from a "principal bundle" construction, where the total space is a quasi-associative deformation of a 3-dimensional Heisenberg manifold.

Abstract:
Let $Z$ be a closed subscheme of a smooth complex projective variety $Y\subseteq \Ps^N$, with $\dim\,Y=2r+1\geq 3$. We describe the intermediate N\'eron-Severi group (i.e. the image of the cycle map $A_r(X)\to H_{2r}(X;\mathbb{Z})$) of a general smooth hypersurface $X\subset Y$ of sufficiently large degree containing $Z$.

Abstract:
Let $C\subset \bold P^r$ be an integral projective curve. One defines the speciality index $e(C)$ of $C$ as the maximal integer $t$ such that $h^0(C,\omega_C(-t))>0$, where $\omega_C$ denotes the dualizing sheaf of $C$. Extending a classical result of Halphen concerning the speciality of a space curve, in the present paper we prove that if $C\subset \bold P^5$ is an integral degree $d$ curve not contained in any surface of degree $< s$, in any threefold of degree $>s>>t>>u\geq 1$, then $ e(C)\leq {\frac{d}{s}}+{\frac{s}{t}}+{\frac{t}{u}}+u-6. $ Moreover equality holds if and only if $C$ is a complete intersection of hypersurfaces of degrees $u$, ${\frac{t}{u}}$, ${\frac{s}{t}}$ and ${\frac{d}{s}}$. We give also some partial results in the general case $C\subset \bold P^r$, $r\geq 3$.