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Maximal exterior sets of hyperbolic quadrics: The complete classification
1991
Journal of combinatorial theory. Series A
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MAXIMAL EXTERIOR SETS An exterior set with respect to the hyperbolic quadric Q+(2n -1, q) of PG(2n -1, q), IZ # 2, is a set X of points such that each line joining two distinct elements of X has no point ...
An exterior set with respect to the hyperbolic quadric Q'(2n-1, q) of PG(2n -1, q), n 3 2, is a set X of points such that each line joining two distinct elements of X has no point in common with Q+(2n- ...
MAXIMAL EXTERIOR SETS An exterior set with respect to the hyperbolic quadric Q+(2n -1, q) of PG(2n -1, q), IZ # 2, is a set X of points such that each line joining two distinct elements of X has no point ...
doi:10.1016/0097-3165(91)90040-n
fatcat:i5veheewtngchgxyml2iwhracy
On the number of components of a complete intersection of real quadrics
[article]
2012
arXiv
pre-print
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We prove that the maximal number $B^0_2(N)$ of connected components that a regular complete intersection of three real quadrics in $\Bbb{P}^N$ can have differs at most by one from the maximal number of ...
Our main results concern complete intersections of three real quadrics. ...
In particular, the maximal number of connected components of a complete intersection of three real quadrics in P 5 R equals 10 = Hilb(6) + 1. ...
arXiv:0806.4077v3
fatcat:ocgzf6e4tvfnvd3stjglfdfa5m
Projection pencil of quadrics and Ivory theorem
[article]
2009
arXiv
pre-print
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The "confocality property" of stachel can be get from our definition in the case when the projection transformation is regular, it is the identity transformation of the space. ...
Our observation is that the generalized definition of confocality in stachel does not give back to the original definition of confocality of Euclidean conics. ...
Definition 1 A maximal set of quadrics called by pencil of quadrics if the selfadjoint linear transformations corresponding their duals belong a two-dimensional subspace of the vector space L(V ). ...
arXiv:0905.4093v1
fatcat:cuscuu6slvcc7d3xhvw5rwekmm
Real algebraic curves of bidegree (5,5) on the quadric ellipsoid
[article]
2020
arXiv
pre-print
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We complete the topological classification of real algebraic non-singular curves of bidegree (5, 5) on the quadric ellipsoid. ...
We show in particular that previously known restrictions form a complete system for this bidegree. Therefore, the main part of the paper concerns the construction of real algebraic curves. ...
The real part RX of X is the set of points fixed by σ. ...
arXiv:1809.03946v2
fatcat:uymqxzjinrbtjhjuo4xr6q7yjy
Floer cohomology and pencils of quadrics
[article]
2011
arXiv
pre-print
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We construct a derived equivalence between the Fukaya category of a curve and the nilpotent summand of the Fukaya category of the associated complete intersection of two quadrics. ...
There is a classical relationship in algebraic geometry between a hyperelliptic curve and an associated pencil of quadric hypersurfaces. ...
For completeness, we discuss quadrics of both even and odd dimension.
Lemma 4.1. ...
arXiv:1006.1099v3
fatcat:2kfpvtwakjhytmgiwxcowmchai
On the Number of Components of a Complete Intersection of Real Quadrics
[chapter]
2011
PROGRESS IN MATHEMATICS
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We prove that the maximal number B 0 2 (N ) of connected components that a regular complete intersection of three real quadrics in P N can have differs at most by one from the maximal number of ovals of ...
Our main results concern complete intersections of three real quadrics. ...
In particular, the maximal number of connected components of a complete intersection of three real quadrics in P 5 R equals 10 = Hilb(6) + 1. ...
doi:10.1007/978-0-8176-8277-4_5
fatcat:p6paec7tnrbptp72zdjpcgmwfm
Codes Associated with Nondegenerate Quadrics of a Symplectic Space of Even Order
2001
Journal of combinatorial theory. Series A
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This paper studies the incidence relation between the points and quadrics in the projective space of a symplectic vector space over a field of even order. ...
The 2-rank of the incidence matrix is determined. ...
ACKNOWLEDGMENT We take this opportunity to thank the referee for several suggestions which have improved the exposition. ...
doi:10.1006/jcta.2000.3118
fatcat:noourjw545h4viel2wa6azpa34
Bigraded Equivariant Cohomology of Real Quadrics
[article]
2006
arXiv
pre-print
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We give a complete description of the bigraded Bredon cohomology ring of smooth projective real quadrics, with coefficients in the constant Mackey functor Z . ...
Some of the results and techniques introduced can be applied to other geometrically cellular real varieties. ...
Left to the reader.
Isotropic quadrics Consider a real quadratic form q of rank n + 2 that can be written as q = q ′ + h, where h is a hyperbolic factor. ...
arXiv:math/0605711v1
fatcat:lpjlvgssffeyffhslh7wktkqg4
Birational geometry of quadrics in characteristic $2$
2008
Journal of Algebraic Geometry
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The theory of quadratic forms can be regarded as studying an important special case of the general problem of birational classification of algebraic varieties. ...
As in other advances on quadratic forms over the past decade, the proofs use the Chow groups of algebraic cycles on quadrics and products of quadrics. ...
We want to compute the total index (maximal dimension of an isotropic subspace) of s over the function field E/F of the corresponding projective quadric S. ...
doi:10.1090/s1056-3911-08-00472-4
fatcat:h7wp2hdp4fbt7p6stsf6oxwymu
Bianchi's Bäcklund transformation for higher dimensional quadrics
[article]
2008
arXiv
pre-print
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The starting point of our investigation is the higher dimensional (infinitesimal) version of Bianchi's main four theorems on the theory of deformations of quadrics and Bianchi's treatment of the Bäcklund ...
We provide a generalization of Bianchi's Bäcklund transformation from 2-dimensional quadrics to higher dimensional quadrics. ...
on the preservation under the Ivory affinity of lengths of segments between confocal quadrics were already known to other authors; for example Henrici's construction of the articulated hyperbolic paraboloid ...
arXiv:0808.2007v2
fatcat:qxqkg7balbgbzb2y3ojp7lsumm
Intersection of quadrics in C^n, moment-angle manifolds, complex manifolds and convex polytopes
[article]
2018
arXiv
pre-print
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in an open set in complex projective space mathbb P_ C^n-1 ...
It is an overview of different properties of a class of non-Kähler compact complex manifolds called LVMB manifolds, obtained as the Hausdorff space of leaves of systems of commuting complex linear equations ...
different aspects of the subject of these notes with me during several years. ...
arXiv:1807.00838v1
fatcat:hwllfoso2fabtmpq7vknxvubje
The Method of Archimedes in the geometry of quadrics
[article]
2006
arXiv
pre-print
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letter and may provide the key to generalizations in other settings. ...
Certain metric-projective properties of confocal quadrics (most of them established in the first half of the XIX^th century) carry out (stick and transfer) by rolling to and influence surfaces applicable ...
A •−1 (Ao + B) = 0, Q(o) = 0, equivalent to o = −A •−1 B + B T A •−1 B−C 2v T B v (o Complete a maximal set of orthonormal eigenvectors of A to an orthonormal basis of C n and consider the vectors of this ...
arXiv:math/0612375v1
fatcat:qyt6legcg5bo7p4mnnvbffvty4
Stabilizers of subspaces under similitudes of the Klein quadric, and automorphisms of Heisenberg algebras
2012
Linear Algebra and its Applications
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We determine the groups of automorphisms and their orbits for nilpotent Lie algebras of class 2 and small dimension, over arbitrary fields (including the characteristic 2 case). ...
Acknowledgements The authors owe Norbert Knarr at least one cup of coffee for the simple computational arguments in 3.6 (replacing much deeper arguments involving Witt cancellation and the Skolem-Noether ...
The second author was supported by SFB 478 "Geometrische Strukturen in der Mathematik", Münster, Germany; a substantial part of this paper was written during a stay at Münster in 2009. ...
doi:10.1016/j.laa.2012.03.018
fatcat:g6mqabg2j5da7bcphaidjracuq
Page 4316 of Mathematical Reviews Vol. , Issue 87h
[page]
1987
Mathematical Reviews
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By definition a maximal exterior set is a set of g? +q+1 points such that any line joining two elements of the set is exterior to the quadric. ...
(B-GHNT-G) Exterior sets with respect to the hyperbolic quadric in PG(2n-—1,q).
Finite geometries (Winnipeg, Man., 1984), 83-89, Lecture Notes in Pure and Appl. Math., 103, Dekker, New York, 1985. ...
Page 3337 of Mathematical Reviews Vol. , Issue 94f
[page]
1994
Mathematical Reviews
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This article also discusses some new results on partial flocks and maximal exterior sets of hyperbolic quadrics in PG(2m — 1, q).
{For the entire collection see MR 93m:00039.}
Gary L. ...
the hyperbolic quadric in PG(3, q). ...
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