1,649 research outputs found
Geometries arising from trilinear forms on low-dimensional vector spaces
No full textLet Gk(V) be the k-Grassmannian of a vector space V with dimV=n. Given a hyperplane H of Gk(V), we define in [I. Cardinali, L. Giuzzi, A. Pasini, A geometric approach to alternating k-linear forms, J. Algebraic Combin. doi: 10.1007/s10801-016-0730-6] a point-line subgeometry of PG(V) called the geometry of poles of H. In the present paper, exploiting the classification of alternating trilinear forms in low dimension, we characterize the possible geometries of poles arising for k=3 and n≤7 and propose some new constructions. We also extend a result of [J.Draisma, R. Shaw, Singular lines of trilinear forms, Linear Algebra Appl. doi: 10.1016/j.laa.2010.03.040] regarding the existence of line spreads of PG(5,K) arising from hyperplanes of G3(V)
La Pinacologia. Appunti metodologici (in Cardinali M, De Ruggieri MB, Ferdinando Perez e la nascita dei laboratori scientifici museali)
No full textLine polar Grassmann codes of orthogonal type
No full textPolar Grassmann codes of orthogonal type have been introduced in I. Cardinali and L. Giuzzi, \emph{Codes and caps from orthogonal Grassmannians}, {Finite Fields Appl.} {\bf 24} (2013), 148-169. They are subcodes of the Grassmann code arising from the projective system defined by the Pl\"ucker embedding of a polar Grassmannian of orthogonal type. In the present paper we fully determine the minimum distance of line polar Grassmann Codes of orthogonal type for q odd
Bioinformatics as an Increasingly Important Resource in Taxonomy, Phylogenetic and Diagnostic
No full textOn the Grassmann module of symplectic dual polar spaces of rank 4 in characteristic 3
No full textLet V be the Weyl module of dimension (2n n) - (2n n-2) for the symplectic group Sp(2n, F) whose highest weight is the nth fundamental dominant weight. The module V affords the grassmann embedding of the symplectic dual polar space DW (2n - 1, F), therefore V is also called the grassmann module for the symplectic group.
We consider the smallest case for char(F) odd for which V is reducible, namely n = 4 and char(F) = 3. In this case the unique factor R of V has vector dimension I. Here we provide a geometric description for Rand study some relations between Rand other objects associated with the grassmann embedding. (C) 2009 Elsevier B.V. All rights reserved
Relazioni tra una multifunzione e la sua frontiera
No full textDenote by "frF" the multivalued mapping defined as the boundary of F. In the paper, in the setting T topological space and X is a topological linear space, the author studies the connection existing between the lower [respectively, upper] semicontinuity of the multivalued mapping F, and the lower [respectively, upper] semicontinuity of "frF". This paper can be seen as an extension of a previous work by the author and F. Papalini
Embeddings of Line-grassmannians of Polar Spaces in Grassmann Varieties
No full textAn embedding of a point-line geometry is usually defined as an injective mapping from the
point-set of to the set of points of a projective space such that is a projective line
for every line of . However, different situations are considered in the literature, where
is allowed to be a subline of a projective line or a curve. In this paper we propose a more
general definition of embedding which includes all the above situations and we focus on a class of embeddings,
which we call Grassmann embeddings, where the points of are firstly associated to lines of a projective
geometry , next they are mapped onto points of via the usual projective
embedding of the line-grassmannian of in . In the central part of our
paper we study sets of points of corresponding to lines of totally
singular for a given alternating, hermitian or quadratic form of . Finally, we apply the results obtained in that part to the
investigation of Grassmann embeddings of several generalized quadrangles
Impure aspects of supersymmetric Wilson loops
No full textWe study a general class of supersymmetric Wilson loops operator in N = 4 super Yang-Mills theory, obtained as orbits of conformal transformations. These loops are the natural generalization of the familiar circular Wilson-Maldacena operator and their supersymmetric properties are encoded into a Killing spinor that is not pure. We present a systematic analysis of their scalar couplings and of the preserved supercharges, modulo the action of the global symmetry group, both in the compact and in the non-compact case. The quantum behavior of their expectation value is also addressed, in the simplest case of the Lissajous contours: explicit computations at weak-coupling, through Feynman diagrams expansion, and at strong-coupling, by means of AdS/CFT correspondence, suggest the possibility of an exact evaluation
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