共查询到20条相似文献,搜索用时 31 毫秒
1.
Jon Eivind Vatne 《Annali dell'Universita di Ferrara》2012,58(1):199-215
In this paper we study Cohen–Macaulay monomial multiple structures (non-reduced schemes) on a linear subspace of codimension
two in projective space. We show that these structures determine smooth points in their respective Hilbert schemes, with (smooth)
neighbourhoods of two such points intersecting if their Hilbert functions are equal. We generalize a construction for multiple
structures on points in the plane to this setting, giving a kind of product of monomial multiple structures. For points, this
construction can be found in Nakajima’s book (Lectures on Hilbert schemes of points on surfaces, Univ Lecture Ser AMS, vol
18, 1999). The tools we use for studying multiple structures are developed in Vatne (Math Nachr 281(3):434–441, 2008; Comm Algebra 37(11):3861–3873, 2009) (see also Vatne in Towards a classification of multiple structures, PhD thesis, University of Bergen, 2001). 相似文献
2.
Following the Cartan’s original method of equivalence supported by methods of parabolic geometry, we provide a complete solution for the equivalence problem of quaternionic contact structures, that is, the problem of finding a complete system of differential invariants for two quaternionic contact manifolds to be locally diffeomorphic. This includes an explicit construction of the corresponding Cartan geometry and detailed information on all curvature components. 相似文献
3.
Oleg I. Morozov 《Acta Appl Math》2007,99(3):309-319
We establish relations between Maurer–Cartan forms of symmetry pseudo-groups and coverings of differential equations. Examples
include Liouville’s equation, the Khokhlov–Zabolotskaya equation, and the Boyer–Finley equation.
相似文献
4.
Jesse Alt 《Annals of Global Analysis and Geometry》2011,39(2):165-186
We apply the theory of Weyl structures for parabolic geometries developed by Čap and Slovák (Math Scand 93(1):53–90, 2003)
to compute, for a quaternionic contact (qc) structure, the Weyl connection associated to a choice of scale, i.e. to a choice
of Carnot–Carathéodory metric in the conformal class. The result of this computation has applications to the study of the
conformal Fefferman space of a qc manifold, cf. (Geom Appl 28(4):376–394, 2010). In addition to this application, we are also
able to easily compute a tensorial formula for the qc analog of the Weyl curvature tensor in conformal geometry and the Chern–Moser
tensor in CR geometry. This tensor was first discovered via different methods by Ivanov and Vasillev (J Math Pures Appl 93:277–307,
2010), and we also get an independent proof of their Local Sphere Theorem. However, as a result of our derivation of this
tensor, its fundamental properties—conformal covariance, and that its vanishing is a sharp obstruction to local flatness of
the qc structure—follow as easy corollaries from the general parabolic theory. 相似文献
5.
In this paper, we develop the theoretical foundations of discrete Dirac mechanics, that is, discrete mechanics of degenerate
Lagrangian/Hamiltonian systems with constraints. We first construct discrete analogues of Tulczyjew’s triple and induced Dirac
structures by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this
framework provides a means of deriving discrete Lagrange–Dirac and nonholonomic Hamiltonian systems. In particular, this yields
nonholonomic Lagrangian and Hamiltonian integrators. We also introduce discrete Lagrange–d’Alembert–Pontryagin and Hamilton–d’Alembert
variational principles, which provide an alternative derivation of the same set of integration algorithms. The paper provides
a unified treatment of discrete Lagrangian and Hamiltonian mechanics in the more general setting of discrete Dirac mechanics,
as well as a generalization of symplectic and Poisson integrators to the broader category of Dirac integrators. 相似文献
6.
Fumiharu Kato 《Mathematische Zeitschrift》2008,259(3):631-641
We give an explicit construction of a unitary Shimura surface that has Mumford’s fake projective plane as one of its connected
components. Moreover, as a byproduct of the construction, we show that Mumford’s fake projective place has a model defined
over the 7th cyclotomic field. 相似文献
7.
Robert Clancy 《Annals of Global Analysis and Geometry》2011,40(2):203-222
We find new examples of compact Spin(7)-manifolds using a construction of Joyce (J. Differ. Geom., 53:89–130, 1999; Compact manifolds with special holonomy. Oxford University Press, Oxford, 2000). The essential ingredient in Joyce’s construction is a Calabi–Yau 4-orbifold with particular singularities admitting an
antiholomorphic involution, which fixes the singularities. We search the class of well-formed quasismooth hypersurfaces in
weighted projective spaces for suitable Calabi–Yau 4-orbifolds. 相似文献
8.
A. Albouy 《Regular and Chaotic Dynamics》2008,13(6):525-542
We show that there exists a projective dynamics of a particle. It underlies intrinsically the classical particle dynamics
as projective geometry underlies Euclidean geometry. In classical particle dynamics a particle moves in the Euclidean space
subjected to a potential. In projective dynamics the position space has only the local structure of the real projective space.
The particle is subjected to a field of projective forces. A projective force is not an element of the tangent bundle to the position space, but of some fibre bundle isomorphic to
the tangent bundle.
These statements are direct consequences of Appell’s remarks on the homography in mechanics, and are compatible with similar
statements due to Tabachnikov concerning projective billiards. When we study Euclidean geometry we meet some particular properties
that we recognize as projective properties. The same is true for the dynamics of a particle. We show that two properties in
classical particle dynamics are projective properties. The fact that the Keplerian orbits close after one turn is a consequence
of a more general projective statement. The fact that the fields of gravitational forces are divergence free is a projective
property of these fields.
相似文献
9.
In this paper we solve local CR embeddability problem of smooth CR manifolds into spheres under a certain nondegeneracy condition
on the Chern–Moser’s curvature tensor. We state necessary and sufficient conditions for the existence of CR embeddings as
finite number of equations and rank conditions on the Chern–Moser’s curvature tensors and their derivatives. We also discuss
the rigidity of those embeddings.
J.-W. Oh was partially supported by BK21-Yonsei University. 相似文献
10.
John Loftin 《Geometriae Dedicata》2007,128(1):97-106
F. Labourie and the author independently have shown that a convex real projective structure on an oriented closed surface
S of genus at least two is equivalent to a pair of a conformal structure plus a holomorphic cubic differential. Along certain
paths, we find the limiting holonomy of convex real projective structures on a surface S corresponding corresponding to a given fixed conformal structure S and a holomorphic cubic differential λ U
0 as . We explicitly give part of the data needed to identify the boundary point in Inkang Kim’s compactification of the deformation
space of convex real projective structures. The proof follows similar analysis to that studied by Mike Wolf is his application
of harmonic map theory to reproduce Thurston’s boundary of Teichmüller space.
相似文献
11.
Svatopluk Krýsl 《Differential Geometry and its Applications》2008,26(5):553-565
We give a classification of 1st order invariant differential operators acting between sections of certain bundles associated to Cartan geometries of the so-called metaplectic contact projective type. These bundles are associated via representations, which are derived from the so-called higher symplectic (sometimes also called harmonic or generalized Kostant) spinor modules. Higher symplectic spinor modules are arising from the Segal-Shale-Weil representation of the metaplectic group by tensoring it by finite dimensional modules. We show that for all pairs of the considered bundles, there is at most one 1st order invariant differential operator up to a complex multiple and give an equivalence condition for the existence of such an operator. Contact projective analogues of the well known Dirac, twistor and Rarita-Schwinger operators appearing in Riemannian geometry are special examples of these operators. 相似文献
12.
Kai Johannes Keller Nikolaos A. Papadopoulos Andrés F. Reyes-Lega 《Mathematische Semesterberichte》2008,55(2):149-160
The aim of this paper is to give a simple, geometric proof of Wigner’s theorem on the realization
of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several
proofs exist already, it seems that the relevance of Wigner’s theorem is not fully appreciated in general.
It is Wigner’s theorem which allows the use of linear realizations of symmetries and therefore guarantees
that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical
point of view in order to prove this theorem. It becomes apparent that Wigner’s theorem is nothing else
but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here
is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics. 相似文献
13.
Kai Johannes Keller Nikolaos A. Papadopoulos Andrés F. Reyes-Lega 《Mathematische Semesterberichte》2008,47(10):149-160
The aim of this paper is to give a simple, geometric proof of Wigner’s theorem on the realization
of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several
proofs exist already, it seems that the relevance of Wigner’s theorem is not fully appreciated in general.
It is Wigner’s theorem which allows the use of linear realizations of symmetries and therefore guarantees
that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical
point of view in order to prove this theorem. It becomes apparent that Wigner’s theorem is nothing else
but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here
is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics. 相似文献
14.
We define a quasi–projective reduction of a complex algebraic variety X to be a regular map from X to a quasi–projective variety that is universal with respect to regular maps from X to quasi–projective varieties. A toric quasi–projective reduction is the analogous notion in the category of toric varieties.
For a given toric variety X we first construct a toric quasi–projective reduction. Then we show that X has a quasi–projective reduction if and only if its toric quasi–projective reduction is surjective. We apply this result
to characterize when the action of a subtorus on a quasi–projective toric variety admits a categorical quotient in the category
of quasi–projective varieties.
Received October 29, 1998; in final form December 28, 1998 相似文献
15.
Xiao-Wu Chen 《Archiv der Mathematik》2009,93(1):29-35
Gentle and Todorov proved that in an abelian category with enough projective objects, the extension subcategory of two covariantly
finite subcategories is covariantly finite. We give an example to show that Gentle–Todorov’s theorem may fail in an arbitrary
abelian category; however we prove a triangulated version of Gentle–Todorov’s theorem which holds for arbitrary triangulated
categories; we apply Gentle–Todorov’s theorem to obtain short proofs of a classical result by Ringel and a recent result by
Krause and Solberg.
This project is partially supported by China Postdoctoral Science Foundation (No.s 20070420125 and 200801230). The author
also gratefully acknowledges the support of K. C. Wong Education Foundation, Hong Kong. 相似文献
16.
In this article, we show that the space of nodal rational curves, which is so called a Severi variety (of rational curves), on any non-singular projective surface is always
equipped with a natural Einstein–Weyl structure, if the space is 3-dimensional. This is a generalization of the Einstein–Weyl
structure on the space of smooth rational curves on a complex surface, given by Hitchin. As geometric objects naturally associated to Einstein–Weyl structure,
we investigate null surfaces and geodesics on the Severi varieties. Also, we see that if the projective surface has an appropriate
real structure, then the real locus of the Severi variety becomes a positive definite Einstein–Weyl manifold. Moreover, we
construct various explicit examples of rational surfaces having 3-dimensional Severi varieties of rational curves. 相似文献
17.
R. D. Baker 《Combinatorica》1982,2(2):103-109
IfP is a finite projective plane of ordern with a proper subplaneQ of orderm which is not a Baer subplane, then a theorem of Bruck [Trans. AMS 78(1955), 464–481] asserts thatn≧m
2+m. If the equalityn=m
2+m were to occur thenP would be of composite order andQ should be called a Bruck subplane. It can be shown that if a projective planeP contains a Bruck subplaneQ, then in factP contains a designQ′ which has the parameters of the lines in a three dimensional projective geometry of orderm. A well known scheme of Bruck suggests using such aQ′ to constructP. Bruck’s theorem readily extends to symmetric designs [Kantor, Trans. AMS 146 (1969), 1–28], hence the concept of a Bruck
subdesign. This paper develops the analoque ofQ′ and shows (by example) that the analogous construction scheme can be used to find symmetric designs. 相似文献
18.
We discuss a classical result in planar projective geometry known as Steiners theorem involving 12 interlocking applications of Pappus theorem. We prove this result using three dimensional projective geometry then uncover the dynamics of this construction and relate them to the geometry of the twisted cubic.Mathematics Subject Classification (2000). Primary 51N15. 相似文献
19.
We prove that Fefferman spaces, associated to non-degenerate CR structures of hypersurface type, are characterised, up to
local conformal isometry, by the existence of a parallel orthogonal complex structure on the standard tractor bundle. This
condition can be equivalently expressed in terms of conformal holonomy. Extracting from this picture the essential consequences
at the level of tensor bundles yields an improved, conformally invariant analogue of Sparling’s characterisation of Fefferman
spaces. 相似文献
20.
A structure is said to be ‘Okhuma’ if its automorphism group acts on it uniquely transitively, or slightly generalizing this,
if its automorphism group acts uniquely transitively on each orbit. In this latter case we can think of the orbits as ‘colours’.
Okhuma chains and related structures have been studied by Okhuma and others. Here we generalize their results to coloured
chains, and give some constructions resulting from this of Okhuma graphs and digraphs.
Mathematics Subject Classifications (2000) 06A05, 06F15. 相似文献