1,720,995 research outputs found
Quartic monoid surfaces with maximum number of lines
No full textIn 1884 the German mathematician Karl Rohn published a substantial paper (Rohn, 1884) on the properties of quartic surfaces with triple points, proving (among many other things) that the maximum number of lines contained in a quartic monoid surface is 31. In this paper we study in details this class of surfaces. We prove that there exists an open subset A⊆PK1 (K is a characteristic zero field) that parametrizes (up to a projectivity) all the quartic monoid surfaces with 31 lines; then we study the action of PGL(4,K) on these surfaces, we show that the stabiliser of each of them is a group isomorphic to S3 except for one surface of the family, whose stabiliser is a group isomorphic to S3×C3. Finally, given two quartic surfaces Q(a) and Q(b), with a,b∈A, we show that Q(a) and Q(b) are projectively equivalent if and only if j(a)=j(b), where j is the j-function. To get our results, several computational tools, available in computer algebra systems, are used
A view on extending morphisms from ample divisors
No full textThis article studies the relation between the geometry of a smooth projective variety and that of its hyperplane sections from the viewpoint of Mori theory.
Let X be a smooth projective variety of dimension n≥4 and Y a smooth hyperplane section of X. Thus H2(Y,R)=H2(X,R) by the Lefschetz hyperplane theorem. Let p:Y→Z be a fibration of Y by Fano varieties. The authors prove several results asserting the existence of an extension of p to X under various conditions. In the main case p is the Mori contraction defined by an extremal ray R of the cone of curves NE−−−(Y) of Y in the region KY<0, and p extends iff R is also an extremal ray of NE−−−(X)
Moore–Penrose approach in the Hough transform framework
No full textLet F(x, a) be a real polynomial in two sets of variables, x and a, that is linear with respect to one of the variable sets, say a. In this paper, we deal with two of the main steps of the Hough transform framework for the pattern recognition technique to detect loci in images. More precisely, we present an algorithmic process, based on the Moore–Penrose pseudo-inverse, to provide a region of analysis in the parameter space. In addition, we state an upper bound for the sampling distance of the discretization of the parameter space region
Geometry of the Hough Transforms with Applications to Synthetic Data
No full textIn the framework of the Hough transform technique to detect curves in images, we provide a bound for the number of Hough transforms to be considered for a successful optimization of the accumulator function in the recognition algorithm. Such a bound is consequence of geometrical arguments. We also show the robustness of the results when applied to synthetic datasets strongly perturbed by noise. An algebraic approach, discussed in the appendix, leads to a better bound of theoretical interest in the exact case
r-norm bounds and metric properties for zero loci of real analytic functions
No full textWe consider the problem of deciding whether or not a zero locus, X, of multivariate real analytic functions crosses a given r-norm ball in the real n-dimensional affine space. We perform a local study of the problem, and we provide both necessary and sufficient conditions to answer the question. Our conditions derive from the analysis of differential geometric properties of X at the center of the ball. An algorithm to evaluate r-norms distances is proposed
A note on -bundles as hyperplane sections
No full textLet M be a five-dimensional manifold polarized by a very ample line bundle L. We show that a smooth A in the linear system defined by L cannot be a holomorphic -bundle over a smooth projective 3-fold Y, unless Y is isomorphic to and A is isomorphic to
On manifolds swept out by high dimensional quadrics
No full textWe give a completely different, much shorter, proof of a substantial generalization of the main result from [Y. Kachi and E. Sato, Mem. Amer. Math. Soc. 160 (2002), no. 763, x+116 pp.; MR1938329 (2004g:14058)]. It states that embedded projective n-folds swept out by quadrics of dimension at least [n2]+2 are either scrolls or hyperquadric fibrations, which are also Mori contraction
Image Analysis and Processing – ICIAP 2015: 18th International Conference Genoa, Italy, September 7–11, 2015 Proceedings, Part I
No full text
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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