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1.
Let
be a very ample vector bundle of rank two on a smooth complex projective threefold X. An inequality about the third Segre class of
is provided when
is nef but not big, and when a suitable positive multiple of
defines a morphism X → B with connected fibers onto a smooth projective curve B, where KX is the canonical bundle of X. As an application, the case where the genus of B is positive and
has a global section whose zero locus is a smooth hyperelliptic curve of genus ≧ 2 is investigated, and our previous result
is improved for threefolds.
Received: 27 January 2005; revised: 26 March 2005 相似文献
2.
Kulikov has given an étale morphism of degree d > 1 which is surjective modulo codimension two with X simply connected, settling his generalized jacobian problem. His method reduces the problem to finding a hypersurface and a subgroup of index d generated by geometric generators. By contrast we show that if D has simple normal crossings away from a set of codimension three and meets the hyperplane at infinity transversely, then necessarily d = 1.
Received: 21 November 2006 相似文献
3.
For a nonempty compact set we determine the maximal possible dimension of a subspace of polynomial functions over Ω with degree at most m which possesses a positive basis. The exact value of this maximum depends on topological features of Ω, and we will see that in many of the cases m can be achieved. Whereas only for low m or finite sets Ω it is possible that we have a subspace X with positive basis and with dim X = m + 1. Hence there is no Ω for which a positive basis exists in for all .
This work was accomplished during the 2nd author’s stay in Paris under his Marie Curie fellowship, contract # MEIF-CT-2005-022927. 相似文献
4.
5.
Gülay Karadoğan-Kaya 《Archiv der Mathematik》2007,89(4):315-325
In this paper, we study the structure, deformations and the moduli spaces of complex projective surfaces admitting genus two
fibrations over elliptic curves. We observe that a surface admitting a smooth fibration as above is elliptic, and we employ
results on the moduli of polarized elliptic surfaces to construct moduli spaces of these smooth fibrations. In the case of
nonsmooth fibrations, we relate the moduli spaces to the Hurwitz schemes
of morphisms of degree n from elliptic curves to the modular curve X(d), d ≥ 3. Ultimately, we show that the moduli spaces in the nonsmooth case are fiber spaces over the affine line
with fibers determined by the components of
.
Received: 30 August 2006 相似文献
6.
P. Habegger 《Mathematische Annalen》2008,342(2):449-466
Let be an irreducible closed subvariety defined over . We bound the height of algebraic points on X that are in a certain sense close to the union of all algebraic subgroup of of dimension m < n/dim X. The bound we obtain is effective and will be expressed as a function of the height of X, the degree of X, and n. We then apply this bound to derive certain finiteness results if m is also strictly less than n − dim X. 相似文献
7.
Let X, Y be Banach spaces. We say that a set
is uniformly p–summing if the series
is uniformly convergent for
whenever (xn) belongs to
. We consider uniformly summing sets of operators defined on a
-space and prove, in case X does not contain a copy of c0, that
is uniformly summing iff
is, where T (φ x) = (T#φ) x for all
and x∈X. We also characterize the sets
with the property that
is uniformly summing viewed in
.
Received: 1 July 2005 相似文献
8.
Riccardo Ghiloni 《Mathematische Annalen》2006,335(4):751-766
Let R be a real closed field and let X be an affine algebraic variety over R. We say that X is universally map rigid (UMR for short) if, for each irreducible affine algebraic variety Z over R, the set of nonconstant rational maps from Z to X is finite. A bijective map from an affine algebraic variety over R to X is called weak change of the algebraic structure of X if it is regular and φ−1 is a Nash map, which preserves nonsingular points. We prove the following rigidity theorem: every affine algebraic variety
over R is UMR up to a weak change of its algebraic structure. Let us introduce another notion. Let Y be an affine algebraic variety over R. We say that X and Y are algebraically unfriendly if all the rational maps from X to Y and from Y to X are trivial, i.e., Zariski locally constant. From the preceding theorem, we infer that, if dim (X)≥1, then there exists a set of weak changes of the algebraic structure of X such that, for each t,s ∈ R with t≠s, and are algebraically unfriendly. This result implies the following expected fact: For each (nonsingular) affine algebraic variety
X over R of positive dimension, the natural Nash structure of X does not determine the algebraic structure of X. In fact, the moduli space of birationally nonisomorphic (nonsingular) affine algebraic varieties over R, which are Nash isomorphic to X, has the same cardinality of R. This result was already known under the special assumption that R is the field of real numbers and X is compact and nonsingular.
The author is a member of GNSAGA of CNR, partially supported by MURST and European Research Training Network RAAG 2002–2006
(HPRN–CT–00271). 相似文献
9.
An (n,k)-affine source over a finite field is a random variable X = (X
1,..., X
n
) ∈ , which is uniformly distributed over an (unknown) k-dimensional affine subspace of . We show how to (deterministically) extract practically all the randomness from affine sources, for any field of size larger
than n
c
(where c is a large enough constant). Our main results are as follows:
Research supported by Israel Science Foundation (ISF) grant. 相似文献
1. | (For arbitrary k): For any n,k and any of size larger than n 20, we give an explicit construction for a function D : → , such that for any (n,k)-affine source X over , the distribution of D(X) is ∊-close to uniform, where ∊ is polynomially small in ||. |
2. | (For k=1): For any n and any of size larger than n c , we give an explicit construction for a function D: , such that for any (n, 1)-affine source X over , the distribution of D(X) is ∊-close to uniform, where ∊ is polynomially small in ||. Here, δ>0 is an arbitrary small constant, and c is a constant depending on δ. |
10.
Let X and Y be Banach spaces. We say that a set
(the space of all weakly compact operators from X into Y) is weakly equicompact if, for every bounded sequence (xn) in X, there exists a subsequence (xk(n)) so that (Txk(n)) is weakly uniformly convergent for T ∈ M. We study some properties of weakly equicompact sets and, among other results, we prove: 1) if
is collectively weakly compact, then M* is weakly equicompact iff M** x**={T** x** : T ∈ M} is relatively compact in Y for every x** ∈X**; 2) weakly equicompact sets are precompact in
for the topology of uniform convergence on the weakly null sequences in X.
Received: 14 February 2005; revised: 1 June 2005 相似文献
11.
Adrien Dubouloz 《Mathematische Zeitschrift》2007,255(1):77-93
Given complex algebraic varieties X and Y of the same dimension, the Cancellation Problem asks if an isomorphism between X ×
and Y ×
induces an isomorphism between X and Y. Iitaka and Fujita (J. Fac. Sci. Univ. 24:123–127, 1977) established that the answer is positive for a large class of varieties of any dimension. In 1989, Danielewski constructed a counterexample using smooth rational affine surfaces. His construction was further generalized by Fieseler (Comment. Math. Helvetici 69:5–27, 1994) and Wilkens (C.R. Acad. Sci. Paris Sér. I Math. 326(9):1111–1116, 1998) to describe a larger class of affine surfaces. Here we introduce higher-dimensional analogues of these surfaces. By studying algebraic actions of the additive group
on certain of these varieties, we obtain new counterexamples to the Cancellation Problem in every dimension d ≥ 2. 相似文献
12.
This paper using a geometric approach produces vanishing and nonvanishing results concerning the spaces of twisted symmetric
differentials on subvarieties , with k ≤ m. Emphasis is given to the case of k = m which is special and whose nonvanishing results on the dimensional range dim X > 2/3(N − 1) are related to the space of quadrics containing X and the variety of all tangent trisecant lines of X. The paper ends with an application showing that the twisted symmetric plurigenera, along smooth families of projective varieties Xt are not invariant even for α arbitrarily large.
Received: September 2006, Revision: May 2007, Accepted: June 2007 相似文献
13.
Elói Medina Galego 《Archiv der Mathematik》2007,88(1):52-56
Let X and Y be Banach spaces such that each of them is isomorphic to a complemented subspace of the other. In 1996, W. T. Gowers solved
the Schroeder-Bernstein problem for Banach spaces by showing that X is not necessarily isomorphic to Y . Let (p, q, r, s) be a quadruple in
with p + q ≥ 2 and r + s ≥ 2. Suppose that for every pair of Banach spaces X and Y isomorphic to complemented subspaces of each other and satisfying the following Decomposition Scheme
we conclude that Xm is isomorphic to Yn for some
. In this paper, we show that the discriminant
of this quadruple is different from zero. This result completes the characterization of quadruples in
which are nearly Schroeder-Bernstein Quadruples for Banach spaces.
Received: 10 September 2005 相似文献
14.
After the contributions of Furushima, Nakayama, Peternell and Schneider, in 1993, Furushima [Fur93] finally succeeded in the
classification of the compactifications of the affine 3-space into smooth Fano 3-folds with B2=1. In this paper, we consider the compactifications of the contractible affine 3-folds X (not necessarily X=) into smooth Fano 3-folds V with B2=2. Consequently, we classify all such compactifications X↪(V,D1∪D2) in the case where KV+D1+D2 is not nef. Furthermore, we see that infinitely many mutually non-isomorphic exotic 's can be compactified into Fano 3-folds with B2=2. This phenomenon never occurs when B2=1.
During this research the author was supported as a Twenty-First Century COE Kyoto Mathematics Fellow. 相似文献
15.
Xiong Ping DAI 《数学学报(英文版)》2006,22(1):301-310
Let (X, G(X), m) be a probability space with a-algebra G(X) and probability measure m. The set V in G is called P-admissible, provided that for any positive integer n and positive-measure set Vn∈ contained in V, there exists a Zn∈G such that Zn belong to Vn and 0 〈 m(Zn) 〈 1/n. Let T be an ergodic automorphism of (X, G) preserving m, and A belong to the space of linear measurable symplectic cocycles 相似文献
16.
Prof. Ottmar Loos 《Monatshefte für Mathematik》1978,86(2):107-129
Every Jordan pair
defines an algebraic varietyX containing
as a dense open subset.X is projective (affine) if and only if
is separable (radical). The Picard group ofX is generated by the irreducible factors of the generic norm of
. If
is separable then the automorphism group ofX is the projective group of
. 相似文献
17.
We introduce a notion of energy for harmonic currents of bidegree (1, 1) on a complex K?hler manifold (M, ω). This allows us to define
for positive harmonic currents. We then show that for a lamination with singularities of a compact set in
without directed positive closed currents, there is a unique positive harmonic current which minimizes energy. If X is a compact laminated set in
of class
it carries a unique positive harmonic current T of mass 1. The current T can be obtained by an Ahlfors type construction starting with an arbitrary leaf of X. When X has a totally disconnected set of singularities, contained in a countable union of analytic sets, the above construction
still gives positive harmonic currents.
Received: February 2004 Revision: December 2004 Accepted: June 2005 相似文献
18.
Chong LI Genaro LOPEZ 《数学学报(英文版)》2006,22(3):741-750
Let B (resp. K, BC,KC) denote the set of all nonempty bounded (resp. compact, bounded convex, compact convex) closed subsets of the Banach space X, endowed with the Hausdorff metric, and let G be a nonempty relatively weakly compact closed subset of X. Let B° stand for the set of all F ∈B such that the problem (F, G) is well-posed. We proved that, if X is strictly convex and Kadec, the set KC ∩ B° is a dense Gδ-subset of KC / G. Furthermore, if X is a uniformly convex Banach space, we will prove more, namely that the set B /B° (resp. K / B°, BC /B°, KC / B°) is a-porous in B (resp. K,BC, KC). Moreover, we prove that for most (in the sense of the Baire category) closed bounded subsets G of X, the set K / B° is dense and uncountable in K. 相似文献
19.
Maria Rosaria Enea 《Geometriae Dedicata》1994,51(3):257-286
In this paper we develop a structure theory of algebraic right distributive quasigroups which correspond to closed and connected conjugacy classes
generating algebraic Fischer groups (in the sense of [6]) such that the mappingx x
–1
ax, fora
, is an automorphism of
(as variety). We also give examples of algebraic Fischer groups where this does not happen. It becomes clear that the class of algebraic right distributive quasigroups has nice properties concerning subquasigroups, normal subquasigroups and direct product.We give a complete classification of one- and two-dimensional as well as of minimal algebraic right distributive quasigroups. 相似文献
20.
Jorge L. Arocha Javier Bracho Chaim Goodman-Strauss Luis Montejano 《Archiv der Mathematik》2006,86(2):185-192
We prove that affine configurations of 4 lines in
are topologically and combinatorially homeomorphic to affine configurations of 6 points in
Received: 14 July 2004; revised: 18 February 2005 相似文献