Displaying similar documents to “Global minimal models for endomorphisms of projective space”

Projective invariant metrics and open convex regular cones. I

Fabio Podestà (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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In this work we give a characterization of the projective invariant pseudometric P , introduced by H. Wu, for a particular class of real 𝐂 -manifolds; in view of this result, we study the group of projective transformations for the same class of manifolds and we determine the integrated pseudodistance p of P in open convex regular cones of n , endowed with the characteristic metric.

Projective invariant metrics and open convex regular cones. I

Fabio Podestà (1987)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this work we give a characterization of the projective invariant pseudometric P , introduced by H. Wu, for a particular class of real 𝐂 -manifolds; in view of this result, we study the group of projective transformations for the same class of manifolds and we determine the integrated pseudodistance p of P in open convex regular cones of n , endowed with the characteristic metric.

The minimal resultant locus

Robert Rumely (2015)

Acta Arithmetica

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Let K be a complete, algebraically closed nonarchimedean valued field, and let φ(z) ∈ K(z) have degree d ≥ 2. We study how the resultant of φ varies under changes of coordinates. For γ ∈ GL₂(K), we show that the map γ o r d ( R e s ( φ γ ) ) factors through a function o r d R e s φ ( · ) on the Berkovich projective line, which is piecewise affine and convex up. The minimal resultant is achieved either at a single point in P ¹ K , or on a segment, and the minimal resultant locus is contained in the tree in P ¹ K spanned by the fixed points...

Calculation of the avoiding ideal for Σ 1 , 1

Tamás Terpai (2009)

Banach Center Publications

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We calculate the mapping H * ( B O ; ) H * ( K 1 , 0 ; ) and obtain a generating system of its kernel. As a corollary, bounds on the codimension of fold maps from real projective spaces to Euclidean space are calculated and the rank of a singular bordism group is determined.

Semigroup actions on tori and stationary measures on projective spaces

Yves Guivarc'h, Roman Urban (2005)

Studia Mathematica

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Let Γ be a subsemigroup of G = GL(d,ℝ), d > 1. We assume that the action of Γ on d is strongly irreducible and that Γ contains a proximal and quasi-expanding element. We describe contraction properties of the dynamics of Γ on d at infinity. This amounts to the consideration of the action of Γ on some compact homogeneous spaces of G, which are extensions of the projective space d - 1 . In the case where Γ is a subsemigroup of GL(d,ℝ) ∩ M(d,ℤ) and Γ has the above properties, we deduce that...

On some properties of three-dimensional minimal sets in 4

Tien Duc Luu (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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We prove in this paper the Hölder regularity of Almgren minimal sets of dimension 3 in 4 around a 𝕐 -point and the existence of a point of particular type of a Mumford-Shah minimal set in 4 , which is very close to a 𝕋 . This will give a local description of minimal sets of dimension 3 in 4 around a singular point and a property of Mumford-Shah minimal sets in 4 .

A note on minimal zero-sum sequences over ℤ

Papa A. Sissokho (2014)

Acta Arithmetica

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A zero-sum sequence over ℤ is a sequence with terms in ℤ that sum to 0. It is called minimal if it does not contain a proper zero-sum subsequence. Consider a minimal zero-sum sequence over ℤ with positive terms a , . . . , a h and negative terms b , . . . , b k . We prove that h ≤ ⌊σ⁺/k⌋ and k ≤ ⌊σ⁺/h⌋, where σ = i = 1 h a i = - j = 1 k b j . These bounds are tight and improve upon previous results. We also show a natural partial order structure on the collection of all minimal zero-sum sequences over the set i∈ ℤ : -n ≤ i ≤ n for any positive...

Gorenstein projective complexes with respect to cotorsion pairs

Renyu Zhao, Pengju Ma (2019)

Czechoslovak Mathematical Journal

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Let ( 𝒜 , ) be a complete and hereditary cotorsion pair in the category of left R -modules. In this paper, the so-called Gorenstein projective complexes with respect to the cotorsion pair ( 𝒜 , ) are introduced. We show that these complexes are just the complexes of Gorenstein projective modules with respect to the cotorsion pair ( 𝒜 , ) . As an application, we prove that both the Gorenstein projective modules with respect to cotorsion pairs and the Gorenstein projective complexes with respect to cotorsion...

A Note on Lax Projective Embeddings of Grassmann Spaces

Eva Ferrara Dentice (2018)

Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche

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In the paper (Ferrara Dentice et al., 2004) a complete exposition of the state of the art for lax embeddings of polar spaces of finite rank 3 is presented. As a consequence, we have that if a Grassmann space G of dimension 3 and index 1 has a lax embedding in a projective space over a skew–field K , then G is the Klein quadric defined over a subfield of K . In this paper, I examine Grassmann spaces of arbitrary dimension d 3 and index h 1 having a lax embedding in a projective space.

Coloring ordinals by reals

Jörg Brendle, Sakaé Fuchino (2007)

Fundamenta Mathematicae

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We study combinatorial principles we call the Homogeneity Principle HP(κ) and the Injectivity Principle IP(κ,λ) for regular κ > ℵ₁ and λ ≤ κ which are formulated in terms of coloring the ordinals < κ by reals. These principles are strengthenings of C s ( κ ) and F s ( κ ) of I. Juhász, L. Soukup and Z. Szentmiklóssy. Generalizing their results, we show e.g. that IP(ℵ₂,ℵ₁) (hence also IP(ℵ₂,ℵ₂) as well as HP(ℵ₂)) holds in a generic extension of a model of CH by Cohen forcing, and IP(ℵ₂,ℵ₂) (hence...

Definable stratification satisfying the Whitney property with exponent 1

Beata Kocel-Cynk (2007)

Annales Polonici Mathematici

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We prove that for a finite collection of sets A , . . . , A s k + n definable in an o-minimal structure there exists a compatible definable stratification such that for any stratum the fibers of its projection onto k satisfy the Whitney property with exponent 1.

O-minimal fields with standard part map

Jana Maříková (2010)

Fundamenta Mathematicae

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Let R be an o-minimal field and V a proper convex subring with residue field k and standard part (residue) map st: V → k. Let k i n d be the expansion of k by the standard parts of the definable relations in R. We investigate the definable sets in k i n d and conditions on (R,V) which imply o-minimality of k i n d . We also show that if R is ω-saturated and V is the convex hull of ℚ in R, then the sets definable in k i n d are exactly the standard parts of the sets definable in (R,V).

A note on generalized projections in c₀

Beata Deręgowska, Barbara Lewandowska (2014)

Annales Polonici Mathematici

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Let V ⊂ Z be two subspaces of a Banach space X. We define the set of generalized projections by V ( X , Z ) : = P ( X , Z ) : P | V = i d . Now let X = c₀ or l m , Z:= kerf for some f ∈ X* and V : = Z l (n < m). The main goal of this paper is to discuss existence, uniqueness and strong uniqueness of a minimal generalized projection in this case. Also formulas for the relative generalized projection constant and the strong uniqueness constant will be given (cf. J. Blatter and E. W. Cheney [Ann. Mat. Pura Appl. 101 (1974), 215-227] and...

Characterizing projective general unitary groups PGU 3 ( q 2 ) by their complex group algebras

Farrokh Shirjian, Ali Iranmanesh (2017)

Czechoslovak Mathematical Journal

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Let G be a finite group. Let X 1 ( G ) be the first column of the ordinary character table of G . We will show that if X 1 ( G ) = X 1 ( PGU 3 ( q 2 ) ) , then G PGU 3 ( q 2 ) . As a consequence, we show that the projective general unitary groups PGU 3 ( q 2 ) are uniquely determined by the structure of their complex group algebras.

Finite projective planes, Fermat curves, and Gaussian periods

Koen Thas, Don Zagier (2008)

Journal of the European Mathematical Society

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One of the oldest and most fundamental problems in the theory of finite projective planes is to classify those having a group which acts transitively on the incident point-line pairs (flags). The conjecture is that the only ones are the Desarguesian projective planes (over a finite field). In this paper, we show that non-Desarguesian finite flag-transitive projective planes exist if and only if certain Fermat surfaces have no nontrivial rational points, and formulate several other equivalences...

Zero-set property of o-minimal indefinitely Peano differentiable functions

Andreas Fischer (2008)

Annales Polonici Mathematici

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Given an o-minimal expansion ℳ of a real closed field R which is not polynomially bounded. Let denote the definable indefinitely Peano differentiable functions. If we further assume that ℳ admits cell decomposition, each definable closed subset A of Rⁿ is the zero-set of a function f:Rⁿ → R. This implies approximation of definable continuous functions and gluing of functions defined on closed definable sets.