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1.
LetX be a smooth irreducible projective variety over an algebraically closed fieldK andE a vector bundle onX. We prove that, if dimX ≥ 1, there exist a smooth irreducible projective varietyZ overK, a surjective separable morphismf:ZX which is finite outside an algebraic subset of codimension ≥ 3 inX and a line bundleL onX such that the direct image ofL byf is isomorphic toE. WhenX is a curve, we show thatZ, f, L can be so chosen thatf is finite and the canonical mapH 1(Z, O) →H 1(X, EndE) is surjective. Dedicated to the memory of Professor K G Ramanathan  相似文献   

2.
Let X be a smooth projective variety over ? and L be a nef-big divisor on X. Then (X, L) is called a quasi - polarized manifold. Then we conjecture that g(L)q(X), where g(L) is the sectional genus of L and q(X) = dim H1(Ox) is the irregularity of X. In general it is unknown that this conjecture is true or not even in the case of dim X = 2. For example, this conjecture is true if dim X = 2 and dim H(L) > 0. But it is unknown if dim X ≥ 3 and dim H0(L) > 0. In this paper, we consider a lower bound for g(L) if dim X = 2, dim H0(L) ≥ 2, and k(X) ≥ 0. We obtain a stronger result than the above conjecture if dim Bs|L| ≤ 0 by a new method which can be applied to higher dimensional cases. Next we apply this method to the case in which dim X = n ≥ 3 and we obtain a lower bound for g(L) if dim X = 3, dim H0(L) ≥ 2, and k(X) ≥ 0.  相似文献   

3.
Let X be a Banach space. Let Hw*(X*) the Fréchet space whose elements are the holomorphic functions defined on X* whose restrictions to each multiple mB(X*), m = 1,2, …, of the closed unit ball B(X*) of X* are continuous for the weak-star topology. A fundamental system of norms for this space is the supremum of the absolute value of each element of Hw*(X*) in mB(X*), m = 1,2,…. In this paper we construct the bidual of l1 when this space contains no copy of l1. We also show that if X is an Asplund space, then Hw*(X*) can be represented as the projective limit of a sequence of Banach spaces that are Asplund.  相似文献   

4.
Let H = X? R A denote an R-smash product of the two bialgebras X and A. We prove that (X,A) is a pair of matched bialgebras, if the R-smash product H has a braiding structure. When X is an associative algebra and A is a Hopf algebra, we investigate the global dimension and the weak dimension of the smash product H = X? R A and show that lD(H) ≤ rD(A) + lD(X) and wD(H) ≤ wD(A) + wD(X). As an application, we get lD(H 4) = ∞ for Sweedler's four dimensional Hopf algebra H 4. We also study the associativity of smash products and the relations between smash products and factorization for algebras.  相似文献   

5.
We show the nonvanishing of H 0(X,−K X ) for any a Fano 3-fold X for which −K X is a multiple of another Weil divisor in Cl(X). The main case we study is Fano 3-folds with Fano index 2: that is, 3-folds X with rank Pic(X)=1, -factorial terminal singularities and −K X  = 2A for an ample Weil divisor A. We give a first classification of all possible Hilbert series of such polarised varieties (X,A) and deduce both the nonvanishing of H 0(X,−K X ) and the sharp bound (−K X )3≥ 8/165. We find the families that can be realised in codimension up to 4.  相似文献   

6.
Summary LetX be a complex manifold of dimensiond≥3 andH an ample divisor onX. In this paper the global sections of the sheafA X(n(K X +(d-2)H)) are studied whenn∈Z, this generalizing a result by A. J. Sommese.
Riassunto SiaX una varietà complessa di dimensioned≥3 eH un divisore ampio suX. In questo articolo vengono studiate le sezioni globali del fascioA X(n(K X +(d-2)H)), doven∈Z. Cià permette di generalizzare un risultato di A. J. Sommese.
  相似文献   

7.
Let H be a Hopf algebra with bijective antipode, α, β ∈ Aut Hopf (H) and M a finite dimensional (α, β)-Yetter-Drinfeld module. We prove that End(M) endowed with certain structures becomes an H-Azumaya algebra, and the set of H-Azumaya algebras of this type is a subgroup of BQ(k, H), the Brauer group of H.  相似文献   

8.
Wenxu Ge  Hongbo Lv 《代数通讯》2013,41(7):2418-2432
Let H be a hereditary algebra of Dynkin type D n over a field k and 𝒞 H be the cluster category of H. Assume that n ≥ 5 and that T and T′ are tilting objects in 𝒞 H . We prove that the cluster-tilted algebra Γ = End𝒞 H (T)op is isomorphic to Γ′ = End𝒞 H (T′)op if and only if T = τ i T′ or T = στ j T′ for some integers i and j, where τ is the Auslander–Reiten translation and σ is the automorphism of 𝒞 H defined in Section 4.  相似文献   

9.
A reflexive digraph is a pair (X, ρ), where X is an arbitrary set and ρ is a reflexive binary relation on X. Let End (X, ρ) be the semigroup of endomorphisms of (X, ρ). We determine the group of automorphisms of End (X, ρ) for: digraphs containing an edge not contained in a cycle, digraphs consisting of arbitrary unions of cycles such that cycles of length ≥2 are pairwise disjoint, and some circulant digraphs (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

10.
Let Λ be a commutative local uniserial ring with radical factor field k. We consider the category S(Λ) of embeddings of all possible submodules of finitely generated Λ-modules. In case Λ=Z/〈pn〉, where p is a prime, the problem of classifying the objects in S(Λ), up to isomorphism, has been posed by Garrett Birkhoff in 1934. In this paper we assume that Λ has Loewy length at least seven. We show that S(Λ) is controlled k-wild with a single control object IS(Λ). It follows that each finite dimensional k-algebra can be realized as a quotient End(X)/End(X)I of the endomorphism ring of some object XS(Λ) modulo the ideal End(X)I of all maps which factor through a finite direct sum of copies of I.  相似文献   

11.
Consider the triangle‐free process, which is defined as follows. Start with G(0), an empty graph on n vertices. Given G(i ‐ 1), let G(i) = G(i ‐ 1) ∪{g(i)}, where g(i) is an edge that is chosen uniformly at random from the set of edges that are not in G(i ? 1) and can be added to G(i ‐ 1) without creating a triangle. The process ends once a maximal triangle‐free graph has been created. Let H be a fixed triangle‐free graph and let XH(i) count the number of copies of H in G(i). We give an asymptotically sharp estimate for ??(XH(i)), for every \begin{align*}1 \ll i \le 2^{-5} n^{3/2} \sqrt{\ln n}\end{align*}, at the limit as n. Moreover, we provide conditions that guarantee that a.a.s. XH(i) = 0, and that XH(i) is concentrated around its mean.© 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011  相似文献   

12.
We show for a finite abelian groupG and any element in the image of the Swan homomorphism sw: that it can be realized as the finiteness obstruction of a finitely dominated connectedCW-complexX with fundamental group π1(X) =G such that π1(X) is equal to the subgroupG 1(X) defined by Gottlieb. This is motivated by the observation that anyH-spaceX satisfies π1(X) =G 1(X) and still the problem is open whether any finitely dominatedH-space is up to homotopy finite.  相似文献   

13.
LetX be a minimal surface of general type and M (X) the set of equivalence classes of complex structures on the differentiable manifold underlyingX; denoting byM x the dimension of M(X) at [X], the point corresponding to the complex structure ofX we consider the problem of finding an upper bound forM x in terms of the basic numerical invariants ofX. The main result is the Castelunovo's bound:M xPg(X)+2q(X) for certain irregular surfaces. We also generalize the above bound to an arbitrary dimension.  相似文献   

14.
Let H be an infinite hyperbolic group with Kazhdan property (T) and let (H,X) denote the Kazhdan constant of H with respect to a generating set X. We prove that infX(H,X)=0, where the infimum is taken over all finite generating sets of H. In particular, this gives an answer to a Lubotzky question.  相似文献   

15.
16.
LetX be a 1-connected space with Moore loop space ΩX. By a well-known theorem of J. W. Milnor and J. C. Moore [7] the Hurewicz homomorphism induces an isomorphism of Hopf algebrasU*X) ⊗Q)→H *X;Q). HereU(−) denotes the universal enveloping algebra and the Lie bracket on π*X) ⊗Q is given by the Samelson product. Assume now thatX is the geometric realization of anr-reduced simplicial set,r≥3. LetL X be a differential graded free Lie algebra over ℤ describing the tame homotopy type ofX according to the theory of [4]. Then the main result of the present paper is the construction of a sequence of morphisms of differential graded algebras betwenU(L X ) and the algebraC U *X)z of normalized cubical chains on ΩX such that the induced morphisms on homology with coefficientsR k are isomorphismsH r-1+l (U(L x );R k ) ≅H r-1+l C U *X);R k ) forl≤k; hereR 0R 1⊆… is a tame ring system, i. e.R k )⊑Q and each primep with 2p−3≤k is invertible inR k . However, it is no longer true that the Pontrjagin algebraH ≤r−1+k (ΩX; R k ) of ΩX in degrees ≤r−1+k is determined by π*X) or by a cofibrant (-fibrant) modelM of π*X) as will be shown by an example. But there is a filtration onH ≤r−1+k (ΩX; R k ) such that the associated graded algebra is isomorphic toH ≤r−1+k (U(M); R k ).This will be proved by using a filtered Lie algebra model ofX constructed from a bigraded model of π*X). Supported by a CNRS grant and PROCOPE Supported by PROCOPE  相似文献   

17.
If P is a pleated plane in 3-dimensional hyperbolic space H 3 and α a geodesic in its intrinsic metric we define B(P,α), the average bending of P in the direction α. We show that if P is a convex pleated plane embedded in H 3 then B(P,α)≤K for some universal K. Furthermore if PΓ is a boundary component of the convex hull of a quasi-Fuchsian group Γ then B(PΓ,α)=B(Γ) almost everywhere, where B(Γ) is a constant times the length of the bending lamination βΓ of the pleated surface X Γ=PΓ/Γ. We use these to prove a number of results about quasi-Fuchsian groups including a universal bound on the Lipschitz constant for the map to infinity and a bound on the length of βΓ by a constant times the Euler characteristic of X Γ. Oblatum 10-X-1996 & 23-V-1997  相似文献   

18.
Let X be a co-H-space of (p − 1)-cell complex with all cells in even dimensions. Then the loop space ΩX admits a retract Ā min(X) that is the evaluation of the functor Ā min on X. In this paper, we determine the homology H *(Ā min(X)) and give the EHP sequence for the spaces Ā min(X).  相似文献   

19.
We study the category 𝒞(X, Y) generated by an exceptional pair (X, Y) in a hereditary category ?. If r = dim k Hom(X, Y) ≥ 1 we show that there are exactly 3 possible types for 𝒞(X, Y), all derived equivalent to the category of finite dimensional modules mod(H r ) over the r-Kronecker algebra H r . In general 𝒞(X, Y) will not be equivalent to a module category. More specifically, if ? is the category of coherent sheaves over a weighted projective line 𝕏, then 𝒞(X, Y) is equivalent to the category of coherent sheaves on the projective line ?1 or to mod(H r ) and, if 𝕏 is wild, then every r ≥ 1 can occur in this way.  相似文献   

20.
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