Search results for " Geometry."

showing 10 items of 2189 documents

Projective spaces on partially ordered sets and Desargues' postulate

1991

We introduce a generalized concept of projective and Desarguean space where points (and lines) may be of different size. Every unitary module yields an example when we take the 1-and 2-generated submodules as points and lines. In this paper we develop a method of constructing a wide range of projective and Desarguean spaces by means of lattices.

Discrete mathematicsPure mathematicsProjective harmonic conjugateCollineationComplex projective spaceProjective spaceGeometry and TopologyProjective planeQuaternionic projective spaceNon-Desarguesian planeProjective geometryMathematicsGeometriae Dedicata
researchProduct

A unified approach to projective lattice geometries

1992

The interest in pursuing projective geometry on modules has led to several lattice theoretic generalizations of the classical synthetic concept of projective geometry on vector spaces.

Discrete mathematicsPure mathematicsProjective harmonic conjugateCollineationDuality (projective geometry)Projective spaceErlangen programGeometry and TopologyProjective differential geometryPencil (mathematics)MathematicsProjective geometryGeometriae Dedicata
researchProduct

Embedding linear spaces with two line degrees in finite projective planes

1986

In this paper we shall classify all finite linear spaces with line degrees n and n-k having at most n2+n+1 lines. As a consequence of this classification it follows: If n is large compared with k, then any such linear space can be embedded in a projective plane of order n−1 or n.

Discrete mathematicsPure mathematicsReal projective lineReal projective planeDuality (projective geometry)Finite geometryProjective spaceLine at infinityGeometry and TopologyFano planeProjective planeMathematicsJournal of Geometry
researchProduct

Elementary (-1)-curves of P-3

2006

In this note we deal with rational curves in P^3 which are images of a line by means of a finite sequence of cubo-cubic Cremona transformations. We prove that these curves can always be obtained applying to the line a sequence of such transformations increasing at each step the degree of the curve. As a corollary we get a result about curves that can give speciality for linear systems of P^3.

Discrete mathematicsSequenceAlgebra and Number TheoryDegree (graph theory)Linear system14C20Finite sequenceMathematics - Algebraic GeometryCorollaryLinear systems fat pointsFamily of curvesLine (geometry)FOS: MathematicsSettore MAT/03 - GeometriaAlgebraic Geometry (math.AG)Computer Science::DatabasesMathematics
researchProduct

Conjugate unstable manifolds and their underlying geometrized Markov partitions

2000

Abstract Conjugate unstable manifolds of saturated hyperbolic sets of Smale diffeomorphisms are characterized in terms of the combinatorics of their geometrized Markov partitions. As a consequence, the relationship between the local and the global point of view is also made explicit.

Discrete mathematicsSmale diffeomorphismsMathematics::Dynamical SystemsMarkov chainInvariant manifoldsGeometrized Markov partitionsPoint (geometry)Geometry and TopologyMathematics::Symplectic GeometryMathematics::Geometric TopologyConjugateMathematicsTopology and its Applications
researchProduct

Estimates of Jacobians by subdeterminants

2002

Let ƒ: Ω → ℝn be a mapping in the Sobolev space W1,n−1(Ω,ℝn), n ≥ 2. We assume that the determinant of the differential matrix Dƒ (x) is nonnegative, while the cofactor matrix D#ƒ satisfies\(|D^\sharp f|^{\frac{n}{{n - 1}}} \in L^P (\Omega )\), where Lp(Ω) is an Orlicz space. We show that, under the natural Divergence Condition on P, see (1.10), the Jacobian lies in Lloc1 (Ω). Estimates above and below Lloc1 (Ω) are also studied. These results are stronger than the previously known estimates, having assumed integrability conditions on the differential matrix.

Discrete mathematicsSpace (mathematics)OmegaDivergenceCombinatoricsSobolev spacesymbols.namesakeMatrix (mathematics)Differential geometryJacobian matrix and determinantsymbolsGeometry and TopologyDifferential (mathematics)Mathematics
researchProduct

Triple planes with $p_g=q=0$

2019

We show that general triple planes with p_g=q=0 belong to at most 12 families, that we call surfaces of type I,..., XII, and we prove that the corresponding Tschirnhausen bundle is direct sum of two line bundles in cases I, II, III, whereas is a rank 2 Steiner bundle in the remaining cases. We also provide existence results and explicit constructions for surfaces of type I,..., VII, recovering all classical examples and discovering several new ones. In particular, triple planes of type VII provide counterexamples to a wrong claim made in 1942 by Bronowski.

Discrete mathematicsSteiner bundleApplied MathematicsGeneral Mathematics010102 general mathematicsprojective varietiesspaceadjunction theorysurfaces01 natural sciences14E20bundlesunstable hyperplanesMathematics - Algebraic GeometryTriple plane0103 physical sciencesFOS: Mathematics010307 mathematical physicsarrangements[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]0101 mathematicsMSc: Primary 14E20 14J60Algebraic Geometry (math.AG)Mathematicscovers
researchProduct

The cup product of Hilbert schemes for K3 surfaces

2003

To any graded Frobenius algebra A we associate a sequence of graded Frobenius algebras A [n] so that there is canonical isomorphism of rings (H *(X;ℚ)[2]) [n] ≅H *(X [n] ;ℚ)[2n] for the Hilbert scheme X [n] of generalised n-tuples of any smooth projective surface X with numerically trivial canonical bundle.

Discrete mathematicsSurface (mathematics)Hilbert series and Hilbert polynomialSequencePure mathematicsMathematics::Commutative AlgebraGeneral Mathematics010102 general mathematics01 natural sciencesCanonical bundlesymbols.namesakeHilbert schemeCup product0103 physical sciencesFrobenius algebrasymbols[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physicsIsomorphism0101 mathematicsComputingMilieux_MISCELLANEOUSMathematicsInventiones Mathematicae
researchProduct

Impact of common property (E.A.) on fixed point theorems in fuzzy metric spaces

2011

We observe that the notion of common property (E.A.) relaxes the required containment of range of one mapping into the range of other which is utilized to construct the sequence of joint iterates. As a consequence, a multitude of recent fixed point theorems of the existing literature are sharpened and enriched.

Discrete mathematicsT57-57.97QA299.6-433Containment (computer programming)Pure mathematicsSequenceApplied mathematics. Quantitative methodsApplied MathematicsFixed-point theoremConstruct (python library)Fuzzy metric space property (E.A.) common property (E.A.) common fixed point generalized fuzzy contractionRange (mathematics)Differential geometryIterated functionSettore MAT/05 - Analisi MatematicaCommon propertyGeometry and TopologyAnalysisMathematics
researchProduct

Fixed Points for Pseudocontractive Mappings on Unbounded Domains

2010

We give some fixed point results for pseudocontractive mappings on nonbounded domains which allow us to obtain generalizations of recent fixed point theorems of Penot, Isac, and Németh. An application to integral equations is given.

Discrete mathematicsT57-57.97QA299.6-433Mathematics::Functional AnalysisApplied mathematics. Quantitative methodsApplied MathematicsFixed-point theoremFixed pointIntegral equationDifferential geometryGeometry and TopologyCoincidence pointAnalysisTopology (chemistry)MathematicsFixed Point Theory and Applications
researchProduct