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Stefano Pasotti

Bio: Stefano Pasotti is an academic researcher from University of Brescia. The author has contributed to research in topics: Holomorphic function & Hyperbolic geometry. The author has an hindex of 5, co-authored 24 publications receiving 69 citations. Previous affiliations of Stefano Pasotti include University of Trento & Catholic University of the Sacred Heart.

Papers
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Journal ArticleDOI
01 Jan 2010
TL;DR: Generalized Clifford parallelisms involving hyperbolic quadrics in projective spaces over suitable quadratic extensions of F are defined with the help of a quaternion skew field H over a field F of arbitrary characteristic.
Abstract: We define generalized Clifford parallelisms in PG ( 3 , F ) with the help of a quaternion skew field H over a field F of arbitrary characteristic. Moreover we give a geometric description of such parallelisms involving hyperbolic quadrics in projective spaces over suitable quadratic extensions of F .

12 citations

Journal ArticleDOI
TL;DR: In this paper, the α-stability for holomorphic triples over curves of genus g = 1 was studied and necessary and sufficient conditions for the moduli space of α-stable triples to be non-empy were given.
Abstract: Here we study the α-stability for holomorphic triples over curves of genus g = 1. We provide necessary and sufficient conditions for the moduli space of α-stable triples to be non-empy and, in these cases, we show that it is smooth and irreducible.

10 citations

Journal ArticleDOI
TL;DR: It is proved that the kinematic parallelisms are always regular in that sense and some results on the group of translations acting transitively on the pointset are deduced.

9 citations

Journal ArticleDOI
TL;DR: In this article, the authors established a correspondence among loops, regular permutation sets and directed graphs with a suitable edge colouring and characterized regular permutations sets and colored graphs giving rise to the same loop, to isomorphic loops and to isotopic loops.
Abstract: We establish a correspondence among loops, regular permutation sets and directed graphs with a suitable edge colouring and characterize regular permutation sets and, respectively, colored graphs giving rise to the same loop, to isomorphic loops and to isotopic loops.

5 citations

Journal ArticleDOI
TL;DR: In this paper, the authors presented a technique for building a new loop starting from the loops (K,+), (P,\widehat{+})} and satisfying suitable conditions, generalizing the construction presented in Zizioli.
Abstract: In this paper we present a technique for building a new loop starting from the loops (K,+), $${(P,\widehat{+})}$$ and (P, +) fulfilling suitable conditions, generalizing the construction presented in Zizioli (J Geom 95(1–2):173–186, 2009) where $${K=\mathbb{Z}_2}$$ or $${K=\mathbb{Z}_3}$$ and (P, +) is an abelian group. We investigate the dependence of the properties of the new loop on the corresponding properties of the initial ones (associativity, Bol condition, automorphic inverse property, Moufang condition), and we provide some examples.

5 citations


Cited by
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Journal ArticleDOI
TL;DR: In this paper, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.
Abstract: This text, drawn from the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-term course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semi-simple rings, Jacobson's theory of the radical representation theory of groups and algebras, prime and semi-prime rings, primitive and semi-primitive rings, division rings, ordered rings, local and semi-local rings, and perfect and semi-perfect rings. By aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation, the author has produced a text which is suitable not only for use in a graduate course, but also for self-study by other interested graduate students. Numerous exercises are also included. This graduate textbook on rings, fields and algebras is intended for graduate students in mathematics.

1,479 citations

Book
01 Jan 2002
TL;DR: In this paper, the value of the variable in each equation is determined by a linear combination of the values of the variables in the equation and the variable's value in the solution.
Abstract: Determine the value of the variable in each equation.

635 citations

Book ChapterDOI
01 Jan 2002
TL;DR: In Part III of this book, it is proved that every Moufang polygon is isomorphic to one of the Moufag polygons described in this chapter.
Abstract: In this chapter, we describe nine families of Moufang polygons. In Part III of this book, we prove that every Moufang polygon is isomorphic to one of the Moufang polygons described in this chapter.

48 citations

Journal ArticleDOI
TL;DR: In this paper, the concept of Clifford parallelism was introduced, which consists of all regular spreads of the real projective 3-space whose focal lines form a regulus contained in an imaginary quadric (D1 = Klein's definition).
Abstract: Parallelity in the real elliptic 3-space was defined by W. K. Clifford in 1873 and by F. Klein in 1890; we compare the two concepts. A Clifford parallelism consists of all regular spreads of the real projective 3-space $${{\rm PG}(3,\mathbb{R})}$$ whose (complex) focal lines (=directrices) form a regulus contained in an imaginary quadric (D1 = Klein’s definition). Our new access to the topic ‘Clifford parallelism’ is free of complexification and involves Klein’s correspondence λ of line geometry together with a bijective map γ from all regular spreads of $${{\rm PG}(3,\mathbb{R})}$$ onto those lines of $${{\rm PG}(5,\mathbb{R})}$$ having no common point with the Klein quadric; a regular parallelism P of $${{\rm PG}(3,\mathbb{R})}$$ is Clifford, if the spreads of P are mapped by γ onto a plane of lines (D2 = planarity definition). We prove the equivalence of (D1) and (D2). Associated with γ is a simple dimension concept for regular parallelisms which allows us to say instead of (D2): the 2-dimensional regular parallelisms of $${{\rm PG}(3,\mathbb{R})}$$ are Clifford (D3 = dimensionality definition). Submission of (D2) to λ−1 yields a complexification free definition of a Clifford parallelism which uses only elements of $${{\rm PG}(3,\mathbb{R})}$$ : A regular parallelism P is Clifford, if the union of any two distinct spreads of P is contained in a general linear complex of lines (D4 = line geometric definition). In order to see (D1) and (D2) simultaneously at work we discuss the following two examples using, at the one hand, complexification and (D1) and, at the other hand, (D2) under avoidance of complexification. Example 1. In the projectively extended real Euclidean 3-space a rotational regular spread with center o is submitted to the group of all rotations about o; we prove, that a Clifford parallelism is generated. Example 2. We determine the group $${Aut_e({\bf P}_{\bf C})}$$ of all automorphic collineations and dualities of the Clifford parallelism P C and show $${Aut_e({\bf P}_{\bf C})\hspace{1.5mm} \cong ({\rm SO}_3\mathbb{R} \times {\rm SO}_3\mathbb{R})\rtimes \mathbb{Z}_2}$$ .

14 citations

Journal ArticleDOI
TL;DR: In this paper, the authors studied coherent systems of type (n, d, k) on the projective line which are stable with respect to some value of a parameter α, and studied the variation of the moduli spaces with α.
Abstract: In this paper, we continue the investigation of coherent systems of type (n, d, k) on the projective line which are stable with respect to some value of a parameter α. We consider the case k = 1 and study the variation of the moduli spaces with α. We determine inductively the first and last moduli spaces and the flip loci, and give an explicit description for ranks 2 and 3. We also determine the Hodge polynomials explicitly for ranks 2 and 3 and in certain cases for arbitrary rank.

10 citations