Solid image extraction from LIDAR point clouds

In laser scanner architectural surveying it is necessary to extract orthogonal projections from the tridimensional model, plans, elevations and cross sections. The paper presents the workflow of architectural drawings production from laser scans, focusing on the orthogonal projection of the point cloud on solid images, in order to avoid the time consuming surface modeling, when it is not strictly necessary. The proposed procedures have been implemented in fortran90 and included in the VELOCE software package, then tested and applied to the case study of the San Pietro church in Porto Venere (SP), integrating the architectural surveying with an existing bathymetric and coastal surveyin

Splitting type, global sections and Chern classes for torsion free sheaves on P^N

In this paper we compare a torsion free sheaf \FF on \PP^N and the free vector bundle \oplus_{i=1}^n\OPN(b_i) having same rank and splitting type. We show that the first one has always "less" global sections, while it has a higher second Chern class. In both cases bounds for the difference are found in terms of the maximal free subsheaves of \FF. As a consequence we obtain a direct, easy and more general proof of the "Horrocks' splitting criterion", also holding for torsion free sheaves, and lower bounds for the Chern classes c_i(\FF(t)) of twists of \FF, only depending on some numerical invariants of \FF. Especially, we prove for rank $n$ torsion free sheaves on \PP^N, whose splitting type has no gap (i.e. $b_i\geq b_{i+1}\geq b_i-1$ for every $i=1, ...,n-1$), the following formula for the discriminant: \Delta(\FF):=2nc_2-(n-1)c_1^2\geq -{1/12}n^2(n^2-1) Finally in the case of rank $n$ reflexive sheaves we obtain polynomial upper bounds for the absolute value of the higher Chern classes c_3(\FF(t)), ..., c_n(\FF(t)), for the dimension of the cohomology modules H^i\FF(t) and for the Castelnuovo-Mumford regularity of \FF; these polynomial bounds only depend only on c_1(\FF), c_2(\FF), the splitting type of \FF and $t$.Comment: Final version, 15 page

Ideals with an assigned initial ideal

The stratum St(J,<) (the homogeneous stratum Sth(J,<) respectively) of a monomial ideal J in a polynomial ring R is the family of all (homogeneous) ideals of R whose initial ideal with respect to the term order < is J. St(J,<) and Sth(J,<) have a natural structure of affine schemes. Moreover they are homogeneous w.r.t. a non-standard grading called level. This property allows us to draw consequences that are interesting from both a theoretical and a computational point of view. For instance a smooth stratum is always isomorphic to an affine space (Corollary 3.6). As applications, in Sec. 5 we prove that strata and homogeneous strata w.r.t. any term ordering < of every saturated Lex-segment ideal J are smooth. For Sth(J,Lex) we also give a formula for the dimension. In the same way in Sec. 6 we consider any ideal R in k[x0,..., xn] generated by a saturated RevLex-segment ideal in k[x,y,z]. We also prove that Sth(R,RevLex) is smooth and give a formula for its dimension.Comment: 14 pages, improved version, some more example

Minimum-weight codewords of the Hermitian codes are supported on complete intersections

Let $\mathcal{H}$ be the Hermitian curve defined over a finite field $\mathbb{F}_{q^2}$. In this paper we complete the geometrical characterization of the supports of the minimum-weight codewords of the algebraic-geometry codes over $\mathcal{H}$, started in [1]: if $d$ is the distance of the code, the supports are all the sets of $d$ distinct $\mathbb{F}_{q^2}$-points on $\mathcal{H}$ complete intersection of two curves defined by polynomials with prescribed initial monomials w.r.t. \texttt{DegRevLex}. For most Hermitian codes, and especially for all those with distance $d\geq q^2-q$ studied in [1], one of the two curves is always the Hermitian curve $\mathcal{H}$ itself, while if $d<q$ the supports are complete intersection of two curves none of which can be $\mathcal{H}$. Finally, for some special codes among those with intermediate distance between $q$ and $q^2-q$, both possibilities occur. We provide simple and explicit numerical criteria that allow to decide for each code what kind of supports its minimum-weight codewords have and to obtain a parametric description of the family (or the two families) of the supports. [1] C. Marcolla and M. Roggero, Hermitian codes and complete intersections, arXiv preprint arXiv:1510.03670 (2015)

Integrating phytosociological and agronomic analysis to support the sustainable management of Mediterranean grasslands

The paper analyses the integration of different methodologies for assessing the grazing value of grasslands, aimed at supporting decisions for their sustainable management, that is, the long term preservation of their productive potential. The attribution of an agronomic value (specific index) to each species can be used for a preliminary evaluation of their productive potential. It can be also considered a first step in the exploitation of data already available from studies made on grasslands using a range of approaches, among them phytosociological tables. A data base file containing a collection of Specific indices for 1796 taxa, based on evaluations made by different authors, who applied the Grazing Value method in a range of environments in the Mediterranean area, has been made available on the web site http://www.agr.unian.it/(download area, ricerca)