Search results for "Differential topology"

showing 10 items of 20 documents

Moduli spaces of rank two aCM bundles on the Segre product of three projective lines

2016

Let P^n be the projective space of dimension n on an algebraically closed field of characteristic 0 and F be the image of the Segre embedding of P^1xP^1xP^1 inside P^7. In the present paper we deal with the moduli spaces of locally free sheaves E on F of rank 2 with h^i(F,E(t))=0 for i=1,2 and each integer t.

14J60 14J45 14D20[MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC]Rank (differential topology)Commutative Algebra (math.AC)01 natural sciences[ MATH.MATH-AC ] Mathematics [math]/Commutative Algebra [math.AC]CombinatoricsMathematics - Algebraic GeometryMathematics::Algebraic Geometry0103 physical sciencesFOS: Mathematics0101 mathematicsProjective testAlgebraic Geometry (math.AG)MathematicsAlgebra and Number TheoryImage (category theory)010102 general mathematicsMathematics - Commutative Algebra16. Peace & justice[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Moduli spaceSegre embeddingMSC: Primary: 14J60; secondary: 14J45; 14D20Product (mathematics)[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physicsJournal of Pure and Applied Algebra
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Rank two aCM bundles on the del Pezzo fourfold of degree 6 and its general hyperplane section

2018

International audience; In the present paper we completely classify locally free sheaves of rank 2 with vanishing intermediate cohomology modules on the image of the Segre embedding $\mathbb{P}^2$ x $\mathbb{P}^2 \subseteq \mathbb{P}^8$ and its general hyperplane sections.Such a classification extends similar already known results regarding del Pezzo varieties with Picard numbers 1 and 3 and dimension at least 3.

Algebra and Number TheoryDegree (graph theory)Image (category theory)010102 general mathematicsDimension (graph theory)MSC: Primary 14J60 ; secondary 14J45Hyperplane sectionRank (differential topology)01 natural sciencesCohomologySegre embedding[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]CombinatoricsAlgebraMathematics::Algebraic GeometryHyperplane0103 physical sciences010307 mathematical physics[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]0101 mathematicsMathematics
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Cardinal invariants of cellular Lindelof spaces

2018

A space X is said to be cellular-Lindelof if for every cellular family $$\mathcal {U}$$ there is a Lindelof subspace L of X which meets every element of $$\mathcal {U}$$ . Cellular-Lindelof spaces generalize both Lindelof spaces and spaces with the countable chain condition. Solving questions of Xuan and Song, we prove that every cellular-Lindelof monotonically normal space is Lindelof and that every cellular-Lindelof space with a regular $$G_\delta $$ -diagonal has cardinality at most $$2^\mathfrak {c}$$ . We also prove that every normal cellular-Lindelof first-countable space has cardinality at most continuum under $$2^{<\mathfrak {c}}=\mathfrak {c}$$ and that every normal cellular-Lindel…

Arhangel’skii TheoremMathematics::General MathematicsDiagonalMathematics::General TopologyRank (differential topology)Space (mathematics)01 natural sciencesCombinatoricsCountable chain conditionCardinalityCardinal inequalityLindelöf spaceFOS: MathematicsContinuum (set theory)0101 mathematicsMathematicsMathematics - General TopologyAlgebra and Number TheoryApplied Mathematics010102 general mathematicsGeneral Topology (math.GN)Nonlinear Sciences::Cellular Automata and Lattice Gases· Elementary submodel010101 applied mathematicsMonotonically normal spaceMathematics::LogicComputational MathematicsLindelöf spaceCountable chain conditionGeometry and TopologyAnalysis
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The constant osculating rank of the Wilking manifold

2008

We prove that the osculating rank of the Wilking manifold V3 = (SO (3) × SU (3)) / U• (2), endowed with the metric over(g, )1, equals 2. The knowledge of the osculating rank allows us to solve the differential equation of the Jacobi vector fields. These results can be applied to determine the area and the volume of geodesic spheres and balls. To cite this article: E. Macias-Virgos et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008). © 2007 Academie des sciences.

CombinatoricsGeodesicDifferential equationMathematical analysisMetric (mathematics)Vector fieldGeneral MedicineRank (differential topology)Constant (mathematics)ManifoldMathematicsOsculating circleComptes Rendus Mathematique
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Semimodular Locally Projective Lattices of Rank 4 from v.Staudt’s Point of View

1981

We consider groups of projectivities in a certain kind of lattices called “Spaces”,also comprising the circle planes, and give theorems of v.Staudtian type, which characterize those Spaces which can be represented by a sublattice of a projective geometry of rank 4.

CombinatoricsMinkowski planeTranslation planeTangentPoint (geometry)Rank (differential topology)Type (model theory)Projective testProjective geometryMathematics
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Numerical bounds for semi-stable families of curves or of certain higher-dimensional manifolds

2005

Given an open subset U U of a projective curve Y Y and a smooth family f : V → U f:V\to U of curves, with semi-stable reduction over Y Y , we show that for a subvariation V \mathbb {V} of Hodge structures of R 1 f ∗ C V R^1f_*\mathbb {C}_V with rank ( V ) &gt; 2 \textrm {rank} (\mathbb {V})&gt;2 the Arakelov inequality must be strict. For families of n n -folds we prove a similar result under the assumption that the ( n , 0 ) (n,0) component of the Higgs bundle of V \mathbb {V} defines a birational map.

CombinatoricsProjective curveAlgebra and Number TheoryReduction (recursion theory)Hodge bundleComponent (group theory)Geometry and TopologyRank (differential topology)MathematicsHiggs bundleJournal of Algebraic Geometry
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Der Satz von Tits für PGL2(R), R ein kommutativer Ring vom stabilen Rang 2

1996

Certain permutation groups on sets with distance relation are characterized as groups of projectivities PGL2(R) on the projective line over a commutative ring R of stable rank 2, thus generalizing a classical result of Tits where R is a field.

CombinatoricsProjective lineField (mathematics)Geometry and TopologyAlgebraic geometryCommutative ringPermutation groupRank (differential topology)MathematicsProjective geometryGeometriae Dedicata
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Soluble groups with their centralizer factor groups of bounded rank

2007

Abstract For a group class X , a group G is said to be a C X -group if the factor group G / C G ( g G ) ∈ X for all g ∈ G , where C G ( g G ) is the centralizer in G of the normal closure of g in G . For the class F f of groups of finite order less than or equal to f , a classical result of B.H. Neumann [Groups with finite classes of conjugate elements, Proc. London Math. Soc. 1 (1951) 178–187] states that if G ∈ C F f , the commutator group G ′ belongs to F f ′ for some f ′ depending only on f . We prove that a similar result holds for the class S r ( d ) , the class of soluble groups of derived length at most d which have Prufer rank at most r . Namely, if G ∈ C S r ( d ) , then G ′ ∈ S d…

CombinatoricsPure mathematicsAlgebra and Number TheoryGroup (mathematics)Bounded functionPrüfer rankOrder (group theory)Rank (differential topology)Conjugate elementCentralizer and normalizerMathematicsJournal of Pure and Applied Algebra
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Rank formulae for factorized groups

1991

The following inequalities for the torsion-free rank r0(G) of the group G=AB and for the p∞-rank rp(G) of the soluble-by-finite group G=AB are stated: $$\begin{gathered} r_0 (G) \leqslant r_0 (A) + r_0 (B) - r_0 (A \cap B), \hfill \\ r_p (G) \leqslant r_p (A) + r_p (B) - r_p (A \cap B). \hfill \\ \end{gathered} $$

CombinatoricsPure mathematicsGroup (mathematics)General MathematicsAlgebra over a fieldRank (differential topology)MathematicsUkrainian Mathematical Journal
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Basic Definitions and Facts

2001

Symbol is treated here as a primitive entity as point or line in geometry. Let Con = {f α : α < β} be a well-ordered set of symbols called a language type. β is an ordinal number. The elements of the above set are called connectives. To each connective f α a natural number α(α) ∈ w called the rank of f α or the arity of f α is assigned. The arity α(α) defines the number of arguments of f α . Thus we speak of nullary, unary, or binary connectives, etc. In the sequel Con is assumed to be fixed but arbitrary.

CombinatoricsSet (abstract data type)Unary operationSymbol (programming)Binary numberOrdinal numberNatural numberRank (differential topology)ArityMathematics
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