一类Hopf曲面上的全纯线丛的上同调

Let X be a non-primary Hopf Surface with Abelian fundamental groupπ_1 (X)(?) Z(?)Z_m, L a line bundle on X, we give a formula for computing the dimension of cohomology H~q(X,Ω~P(L)) and the explicit results for non-primary exceptional Hopf surface.     

Linear Operators Preserving Symplectic Group over a Field Consisting of at Least Four Elements

Suppose F is a field consisting of at least four elements. Let Mn(F) and SP2n(F) be the linear space of all n×n matrices and the group of all 2n×2n symplectic matrices over F, respectively. A linear operator L:M2n(F)→M2n(F) is said to preserve the symplectic group if L(SP2n(F))=SP2n(F). It is shown that L is an invertible preserver of the symplectic group if and only if L takes the form (i) L(X)=QPXP-1 for any X∈M2n(F) or (ii) L(X)=QPXTP-1 for any X∈M2n(F), where Q∈SP2n(F) and P is a generalized symplectic matrix. This generalizes the result derived by Pierce in Canad J. Math., 3(1975), 715-724.     

Generalized wavelets and inversion of the radon transform on the laguerre hypergroup

Let X= Rn+ × R denote the underlying manifold of polyradial functions on the Heisenberg group Hn.We construct a generalized translation on X=Rn+ × R, and establish the Plancherel formula on L2(X,dμ).Using the Gelfand transform we give the condition of generalized wavelets on L2(X,dμ). Moreover, we show the reconstruction formulas for wavelet packet trnasforms and an inversion formula of the Radon transform on X.     

The Structure of Vector Bundles on Non-primary Hopf Manifolds∗

Let X be a Hopf manifold with non-Abelian fundamental group and E be a holomorphic vector bundle over X, with trivial pull-back to Cⁿ ? {0}. The authors show that there exists a line bundle L over X such that E ? L has a nowhere vanishing section. It is proved that in case dim(X) ≥ 3, π^?(E) is trivial if and only if E is filtrable by vector bundles. With the structure theorem, the authors get the cohomology dimension of holomorphic bundle E over X with trivial pull-back and the vanishing of Chern class of E.     

DCI-and CI-Groups of Order p~3

Let G be a finite group and S a subset of G.We define the Cayley digraphX=X(C,S)of G with respect to S bywhere V(X)and E(X)are the vertex-and edge-sets of X,respectively.S is saidto be a CI—subset of G if any graphisomorphism X(G,S)≌X(G,T),where TG,implies that there exists a group automorphism α∈ Aut G such that S~α=T.     

s-REGULAR DIHEDRAL COVERINGS OF THE COMPLETE GRAPH OF ORDER 4

§1. Introduction For a ?nite, simple, and undirected graph X, every edge of X gives rise to a pair ofopposite arcs, and we denote by V (X), E(X), A(X) and Aut(X) the vertex set, the edgeset, the arc set and the automorphism group of X, respectively. …     

AUTOMORPHISM GROUPS OF 4-VALENT CONNECTED CAYLEY GRAPHS OF p-GROUPS

61. IntroductionLet G be a trite grouP and S a subs6t of G such thst 1' S and S = S--1. The Cayleygraph X = Cay(G, S) Of G with respect to S is defined to have vertex set V(X) = G and edgeset E(X) = {(g, ag) I g E G, s E' S}. ~ the defection the following two faCts are obvious:(1) the automorphism group Ant(X) of X contains GR, the right regular representation ofG, as a subgroup, and (2) X is cormected if and only if S generates the group G.FOr a Cayley graph X = Cay(G, S) Of …     

Finite Groups in Which Each Irreducible Character has at Most Two Zeros

Let G be a finite group, Irr(G) denotes the set of irreducible complex characters of G and gG the conjugacy class of G containing element g. A well-known theorem of Burnside([1,Theorem 3.15]) states that every nonlinear X ∈ Irr(G) has a zero on G, that is, an element x (or a conjugacy class xG) of G with X(x) = 0. So, if the number of zeros of character table is very small, we may expect, the structure of group is heavily restricted. For example, [2, Proposition 2.7] claimes that G is a Frobenius group with a complement of order 2 if each row in charcter table has at most one zero (its proof uses the classification of simple groups). In this note, we characterize the finite group G satisfying the following hypothesis:     

Holomorphic Vector Bundle on Hopf Manifolds with Abelian Fundamental Groups

Let X be a Hopf manifolds with an Abelian fundamental group.E is a holomorphic vectorbundle of rank r with trivial pull-back to W=C~n-{0}.We prove the existence of a non-vanishingsection of L(?)E for some line bundle on X and study the vector bundles filtration structure of E.These generalize the results of D.Mall about structure theorem of such a vector bundle E.     

Equicontinuity and Sensitivity of Group Actions*

Let(X, G) be a dynamical system(G-system for short), that is, X is a topological space and G is an infinite topological group continuously acting on X. In the paper,the authors introduce the concepts of Hausdorff sensitivity, Hausdorff equicontinuity and topological equicontinuity for G-systems and prove that a minimal G-system(X, G) is either topologically equicontinuous or Hausdorff sensitive under the assumption that X is a T₃-space and they provide a classification of transitive d...     

Automorphisms of wonderful varieties

Let G be a complex semisimple linear algebraic group, and X a wonderful G-variety. We determine the connected automorphism group Aut⁰(X) and we calculate Luna’s invariants of X under its action.     

A minimal triangulation of complex projective plane admitting a chess colouring of four-dimensional simplices

We construct and study a new 15-vertex triangulation X of the complex projective plane ℂP². The automorphism group of X is isomorphic to S ₄ × S ₃. We prove that the triangulation X is the minimal (with respect to the number of vertices) triangulation of ℂP² admitting a chess colouring of four-dimensional simplices. We provide explicit parametrizations for the simplices of X and show that the automorphism group of X can be realized as a group of isometries of the Fubini-Study metric. We find a 33-vertex subdivision $ \bar X $ \bar X of the triangulation X such that the classical moment mapping μ: ℂP² → Δ² is a simplicial mapping of the triangulation $ \bar X $ \bar X onto the barycentric subdivision of the triangle Δ². We study the relationship of the triangulation X with complex crystallographic groups.     

On the unipotence of autoequivalences of toric complete intersection Calabi–Yau categories

Consider the derived category of coherent sheaves, D ^b (X), on a compact Calabi–Yau complete intersection X in a toric variety. The scope of this work is to establish the (quasi-)unipotence of a class of elements in the group of autoequivalences, Aut(D ^b (X)). This is achieved by associating singularity categories, modelled by matrix factorizations, to the toric data. Each of these triangulated categories is equivalent to the derived category of coherent sheaves on X. The idea is then that, although the singularity categories share the group of autoequivalences, on each category there are elements in Aut(D ^b (X)), whose (quasi-)unipotence relations are easier to see than on the other categories.     

The GIT-Equivalence for G-Line Bundles

Let X be a projective variety with an action of a reductive group G. Each ample G-line bundle L on X defines an open subset X^ss(L) of semi-stable points. Following Dolgachev and Hu, define a GIT-class as the set of algebraic equivalence classes of L's with fixed X^ssL. We show that the GIT-classes are the relative interiors of rational polyhedral convex cones, which form a fan in the G-ample cone. We also study the corresponding variations of quotients X^ss(L)//G. This sharpens results of Thaddeus and Dolgachev-Hu.     

Lower bounds¶for the relative Lusternik–Schnirelmann category

We give estimates of numerical homotopy invariants of the pair (X,X×S ^p ) in terms of homotopy invariants of X. More precisely, we prove that σ ^{p +1} cat(X) + 1 ≤ cat(X,X×S ^p }), that and that e(X,X×S< ^p )=e(X)+1, where σ ^{p +1} cat is the (relative) σ category of Vandembroucq and e is the (relative) Toomer invariant. The proof is based on an extension of Milnor's construction of the classifying space of a topological group to a relative setting (due to Dold and Lashof). Received: 14 October 1998 / Revised version: 5 November 1999     

Splitting off tori and the evaluation subgroup of the fundamental group

Given a spaceX what is the largest torusT ⁿ such thatX is homotopy equivalent toY×T ⁿ We find the answer depends on a simple property of the evaluation subgroup of the fundamental group,G ₁(X). As corollaries we have the Splitting theorem of Conner and Raymond and the fact that the dimension ofX must be greater than the rank ofG ₁(X).     

Note: Combinatorial Alexander Duality—A Short and Elementary Proof

Let X be a simplicial complex with ground set V. Define its Alexander dual as the simplicial complex X ^*={σ⊆V∣V∖σ ∉ X}. The combinatorial Alexander duality states that the ith reduced homology group of X is isomorphic to the (|V|−i−3)th reduced cohomology group of X ^* (over a given commutative ring R). We give a self-contained proof from first principles accessible to a nonexpert.     

Isometry Groups of Proper Hyperbolic Spaces

Let X be a proper hyperbolic geodesic metric space and let G be a closed subgroup of the isometry group Iso(X) of X. We show that if G is not elementary then for every p ∈ (1, ∞) the second continuous bounded cohomology group H²_cb(G, L^p(G)) does not vanish. As an application, we derive some structure results for closed subgroups of Iso(X). Partially supported by Sonderforschungsbereich 611.     

Finite-Dimensional Motives and the Conjectures of Beilinson and Murre

We relate the notion of finite dimensionality of the Chow motive M(X) of a smooth projective variety X (as defined by S. Kimura) with the conjectures of Beilinson, Bloch and Murre on the existence of a filtration on the Chow ring CH*(X). We show (Theorem 3) that finite dimensionality of M(X) implies uniqueness, up to isomorphism, of Murre's decomposition of M(X). Conversely (Theorem 4), Murre's conjecture for X ^m ×X ^m (for a suitable m) implies finite-dimensionality of M(X). We also show (Theorem 7) that, for a surface X with p _g = 0, the motive M(X) is finite-dimensional if and only if the Chow group of 0-cycles of X is finite-dimensional in the sense of Mumford, i.e. iff the Bloch conjecture holds for X.The second named author is a member of GNSAGA of CNR.     

Compact complex homogeneous manifolds with large automorphism groups

Let X be a compact complex homogeneous manifold and let Aut(X) be the complex Lie group of holomorphic automorphisms of X. It is well-known that the dimension of Aut(X) is bounded by an integer that depends only on n=dim X. Moreover, if X is K?hler then dimAut (X)≤n(n+2) with equality only when X is complex projective space. In this article examples of non-K?hler compact complex homogeneous manifolds X are given that demonstrate dimAut(X) can depend exponentially on n. Let X be a connected compact complex manifold of dimension n. The group of holomorphic automorphisms of X, Aut(X), is a complex Lie group [3]. For a fixed n>1, the dimension of Aut(X) can be arbitrarily large compared to n. Simple examples are provided by the Hirzebruch surfaces F _m , m∈N, for which dimAut(F _m )=m+5, see, e.g. [2, Example 2.4.2]. If X is homogeneous, that is, any point of X can be mapped to any other point of X under a holomorphic automorphism, then the dimension of the automorphism group of X is bounded by an integer that depends only on n, see [1, 2, 6]. The estimate given in [2, Theorem 3.8.2] is roughly dimAut(X)≤(n+2) ⁿ . For many classes of manifolds, however, the dimension of the automorphism group never exceeds n(n+2). For example, it follows directly from the classification given by Borel and Remmert [4], that if X is a compact homogeneous K?hler manifold, then dimAut(X)≤n(n+2) with equality only when X is complex projective space P ⁿ . It is an old question raised by Remmert, see [2, p. 99], [6], whether this same bound applies to all compact complex homogeneous manifolds. In this note we show that this is not the case by constructing non-K?hler compact complex homogeneous manifolds whose automorphism group has a dimension that depends exponentially on n. The simplest case among these examples has n=3m+1 and dimAut(X)=3m+3 ^m , so the above conjectured bound is exceeded when n≥19. These manifolds have the structure of non-trivial fiber bundles over products of flag manifolds with parallelizable fibers given as the quotient of a solvable group by a discrete subgroup. They are constructed using the original ideas of Otte [6, 7] and are surprisingly similar to examples found there. Generally, a product of manifolds does not result in an automorphism group with a large dimension relative to n. Nevertheless, products are used in an essential way in the construction given here, and it is perhaps this feature that caused such examples to be previously overlooked. Oblatum 13-X-97 & 24-X-1997