Special Grassmann manifolds $V ^4 _3$ in the projective space $P _7$

Josef Vala

Displaying similar documents to “Special Grassmann manifolds $V_{3}^{4}$ in the projective space $P_{7}$ ”

The projective limit of the $H^{p}$ spaces

J. A. Cima, J. R. Harrington, J. A. Pfaltzgraff (1977)

Colloquium Mathematicae

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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 $\mathbf{C}^{\infty}$ -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 $\mathbb{R}^{n}$ , endowed with the characteristic metric.

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 $\geq 3$ 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 $d\geq 3$ and index $h\geq 1$ having a lax embedding in a 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 Lincei. Matematica e Applicazioni

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Grassmann manifold $V_{3}^{4}$ in the projective space $P_{7}$ with characteristics consisting of a quadric and two planes

Josef Vala (1993)

Mathematica Bohemica

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Some results in the geometry of four-parametric manifolds of three-dimensional spaces in the projective space $P_{7}$ are found. The properties of such a manifold $V_{3}^{4}$ with characteristics consisting of a quadric and two planes are studied. The properties of the manifold dual to $V_{3}^{4}$ are found. Some results in the geometry of linear spaces from [1],[2],[3],[4] are used. The notation of the quantities is the same as in [4].

Generic representations of orthogonal groups: projective functors in the category $ℱ_{q u a d}$

Christine Vespa (2008)

Fundamenta Mathematicae

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We continue the study of the category of functors $ℱ_{q u a d}$ , associated to ₂-vector spaces equipped with a nondegenerate quadratic form, initiated in J. Pure Appl. Algebra 212 (2008) and Algebr. Geom. Topology 7 (2007). We define a filtration of the standard projective objects in $ℱ_{q u a d}$ ; this refines to give a decomposition into indecomposable factors of the first two standard projective objects in $ℱ_{q u a d}$ : $P_{H ₀}$ and $P_{H ₁}$ . As an application of these two decompositions, we give a complete description of the polynomial...

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...

The classical subspaces of the projective tensor products of $ℓ_{p}$ and C(α) spaces, α < ω₁

Elói Medina Galego, Christian Samuel (2013)

Studia Mathematica

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We completely determine the $ℓ_{q}$ and C(K) spaces which are isomorphic to a subspace of $ℓ_{p} \otimes ̂_{π} C (α)$ , the projective tensor product of the classical $ℓ_{p}$ space, 1 ≤ p < ∞, and the space C(α) of all scalar valued continuous functions defined on the interval of ordinal numbers [1,α], α < ω₁. In order to do this, we extend a result of A. Tong concerning diagonal block matrices representing operators from $ℓ_{p}$ to ℓ₁, 1 ≤ p < ∞. The first main theorem is an extension of a result of E. Oja and states...

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...

Monodromy of a family of hypersurfaces

Vincenzo Di Gennaro, Davide Franco (2009)

Annales scientifiques de l'École Normale Supérieure

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Let $Y$ be an $(m + 1)$ -dimensional irreducible smooth complex projective variety embedded in a projective space. Let $Z$ be a closed subscheme of $Y$ , and $δ$ be a positive integer such that $ℐ_{Z, Y} (δ)$ is generated by global sections. Fix an integer $d \geq δ + 1$ , and assume the general divisor $X \in | H^{0} (Y, ℐ_{Z, Y} (d)) |$ is smooth. Denote by $H^{m} {(X; ℚ)}_{⊥ Z}^{van}$ the quotient of $H^{m} (X; ℚ)$ by the cohomology of $Y$ and also by the cycle classes of the irreducible components of dimension $m$ of $Z$ . In the present paper we prove that the monodromy representation on $H^{m} {(X; ℚ)}_{⊥ Z}^{van}$ for the family...

Extremally disconnected resolutions of $T_{0}$ -spaces

A. Błaszczyk (1974)

Colloquium Mathematicae

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A Regular Threefold of General Type with $p_{g}=0$ and $P_{2}=6$

M. Cristina Ronconi (2009)

Bollettino dell'Unione Matematica Italiana

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The range of the bigenus $P_{2}$ is one of the unsolved problems concerning smooth complex projective regular threefolds of general type with $p_{g}=0$ : The examples in the literature have $P_{2}\leq 5$ . In the present paper we present a non-singular threefold with $p_{g}=q_{1}=q_{2}=0$ ; $P_{2}=6$ ; the bicanonical map is stably birational.

Explicit birational geometry of threefolds of general type, I

Jungkai A. Chen, Meng Chen (2010)

Annales scientifiques de l'École Normale Supérieure

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Let $V$ be a complex nonsingular projective 3-fold of general type. We prove $P_{12} (V) : = dim H^{0} (V, 12 K_{V}) > 0$ and $P_{m_{0}} (V) > 1$ for some positive integer $m_{0} \leq 24$ . A direct consequence is the birationality of the pluricanonical map $ϕ_{m}$ for all $m \geq 126$ . Besides, the canonical volume $Vol (V)$ has a universal lower bound $ν (3) \geq \frac{1}{63 \cdot 126^{2}}$ .

Hyperideal polyhedra in hyperbolic 3-space

Xiliang Bao, Francis Bonahon (2002)

Bulletin de la Société Mathématique de France

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A hyperideal polyhedron is a non-compact polyhedron in the hyperbolic $3$ -space $ℍ^{3}$ which, in the projective model for $ℍ^{3} \subset {ℝℙ}^{3}$ , is just the intersection of $ℍ^{3}$ with a projective polyhedron whose vertices are all outside $ℍ^{3}$ and whose edges all meet $ℍ^{3}$ . We classify hyperideal polyhedra, up to isometries of $ℍ^{3}$ , in terms of their combinatorial type and of their dihedral angles.

Twisted cotangent sheaves and a Kobayashi-Ochiai theorem for foliations

Andreas Höring (2014)

Annales de l’institut Fourier

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Let $X$ be a normal projective variety, and let $A$ be an ample Cartier divisor on $X$ . Suppose that $X$ is not the projective space. We prove that the twisted cotangent sheaf $Ω_{X} \otimes A$ is generically nef with respect to the polarisation $A$ . As an application we prove a Kobayashi-Ochiai theorem for foliations: if $ℱ ⊊ T_{X}$ is a foliation such that $det ℱ \equiv i_{ℱ} A$ , then $i_{ℱ}$ is at most the rank of $ℱ$ .

Complex structures on product of circle bundles over complex manifolds

Parameswaran Sankaran, Ajay Singh Thakur (2013)

Annales de l’institut Fourier

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Let ${\bar{L}}_{i} \to X_{i}$ be a holomorphic line bundle over a compact complex manifold for $i = 1, 2$ . Let $S_{i}$ denote the associated principal circle-bundle with respect to some hermitian inner product on ${\bar{L}}_{i}$ . We construct complex structures on $S = S_{1} \times S_{2}$ which we refer to as scalar, diagonal, and linear types. While scalar type structures always exist, the more general diagonal but non-scalar type structures are constructed assuming that ${\bar{L}}_{i}$ are equivariant ${(ℂ^{*})}^{n_{i}}$ -bundles satisfying some additional conditions....

Addendum to “On the $p^{λ}$ problem”

Stephan Baier (2005)

Acta Arithmetica

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Displaying similar documents to “Special Grassmann manifolds V 3 4 in the projective space P 7 ”

Displaying similar documents to “Special Grassmann manifolds $V_{3}^{4}$ in the projective space $P_{7}$ ”