共查询到20条相似文献,搜索用时 11 毫秒
1.
Kazuyoshi Takahashi 《Geometriae Dedicata》1999,77(2):185-201
We investigate ample and spanned rank-2 vector bundles E with k-jet ample determinant on algebraic surfaces S. In paticular, we classify such polarized pairs (S,E) with small second Chern class. The case of c_2(E)=k+1 is a generalization of the result of Ballico and Lanteri. 相似文献
2.
Giulio Cotignoli 《代数通讯》2013,41(7):2564-2573
In the mid 1970s, Hartshorne conjectured that, for all n > 7, any rank 2 vector bundles on ? n is a direct sum of line bundles. This conjecture remains still open. In this paper, we construct indecomposable rank two vector bundles on a large class of Fano toric varieties. Unfortunately, this class does not contain ? n . 相似文献
3.
We study the k-very ampleness of the adjoint bundle K S+det E associated to a k-very ample vector bundle E on an algebraic surface S. We extend the results of Beltrametti and Sommese to the vector bundle case and give the classification of the pairs (S, E) such that the preservation of k-very ampleness fails. 相似文献
4.
Kazuyoshi Takahashi 《Mathematische Nachrichten》2000,212(1):173-190
We study the k‐very ampleness of the adjoint bundle KS + det E associated to a (k — 1)‐very ample vector bundle E with degree greater than or equal to 4k + 5 on an algebraic surface S. We classify polarized surfaces (S, E) which the k‐very ampleness of KS + det E fails. 相似文献
5.
E. Ballico 《Acta Appl Math》1998,53(2):229-245
In this paper we study meromorphic maps between vector bundles on a Riemann surface. We are mainly interested in stable vector bundles. For a huge number of numerical data we prove the existence of a meromorphic map between two vector bundles with a prescribed number of zeroes and a prescribed number of poles. 相似文献
6.
Georg Hein 《代数通讯》2013,41(7):2319-2335
Let X be a smooth variety defined over an algebraically closed field of arbitrary characteristic and 𝒪 X (H) be a very ample line bundle on X. We show that for a semistable X-bundle E of rank two, there exists an integer m depending only on Δ(E) · H dim(X)?2 and H dim(X) such that the restriction of E to a general divisor in |mH| is again semistable. As corollaries, we obtain boundedness results, and weak versions of Bogomolov's Theorem and Kodaira's vanishing theorem for surfaces in arbitrary characteristic. 相似文献
7.
In the present paper we give a very short and easy proof of the speciality lemma for codimension 2 subvarieties, even those that are reducible or non-reduced, in P
n
. Furthermore we give cohomological conditions that force a subcanonical surface in P
4 to be a complete intersection and a rank 2 bundle to split, which generalize the classical First Theorem of Gherardelli. 相似文献
8.
Sandra Di Rocco Andrew J. Sommese 《Transactions of the American Mathematical Society》2004,356(2):587-598
This article shows a number of strong inequalities that hold for the Chern numbers , of any ample vector bundle of rank on a smooth toric projective surface, , whose topological Euler characteristic is . One general lower bound for proven in this article has leading term . Using Bogomolov instability, strong lower bounds for are also given. Using the new inequalities, the exceptions to the lower bounds 4e(S)$"> and e(S)$"> are classified.
9.
Francesco Bottacin 《Mathematische Nachrichten》2000,220(1):33-44
In this paper we prove that the moduli spaces of framed vector bundles over a surface X, satisfying certain conditions, admit a family of Poisson structures parametrized by the global sections of a certain line bundle on X. This generalizes to the case of framed vector bundles previous results obtained in [B2] for the moduli space of vector bundles over a Poisson surface. As a corollary of this result we prove that the moduli spaces of framed SU(r) – instantons on S4 = ℝ4 ∪ {∞} admit a natural holomorphic symplectic structure. 相似文献
10.
José Luis González 《代数通讯》2013,41(4):1456-1465
We prove that the Cox ring of the projectivization P(?) of a rank two toric vector bundle ?, over a toric variety X, is a finitely generated k-algebra. As a consequence, P(?) is a Mori dream space if the toric variety X is projective and simplicial. 相似文献
11.
12.
本文中我们利用 A.Bertram和 B. Feiberg证明的在 g=5的当 S(E)<2时的一般代数曲线上二维特殊稳定向量丛的存在定理作为反例,说明进一步的Maruyama猜想和Arrondo-Sols猜想在g=5的一般代数曲线上均不能成立. 相似文献
13.
Mehmet Kirdar 《K-Theory》1998,13(1):57-59
For 2, we describe the reduced real K-theory K~O(Lk2n)) of the standard lens space Lk(2n)xs in terms of generators and relations. In particular, we show that the K~O-order of the Hopf bundle is 2n–1+2[/2]. 相似文献
14.
Let X be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli scheme of rank-2 bundles. We show that up to isomorphism, there is only one (up to tensoring by an order two line bundle) semi-stable vector bundle of rank 2 (with determinant equal to a theta characteristic) whose Frobenius pull-back is not semi-stable. The indeterminacy of the Frobenius map at this point can be resolved by introducing Higgs bundles. 相似文献
15.
16.
This paper is devoted to the function introduced by M.P. Appell in connection with decomposition of elliptic functions of the third kind into simple elements. We show that this function is related to global sections of rank-2 vector bundles on elliptic curves. We derive analogues of theta-identities for this function and prove the divisibility property for the action of the modular group, that should be considered as a replacement of the functional equation. 相似文献
17.
We consider general surfaces, S, of high degree containing a given complete intersection space curve, Y. We study integral curves in the subgroup of Pic(S) generated by Y and the plane section. We determine the cohomological invariants of these curves and classify the subcanonical ones. Then using these subcanonical curves we produce stable rank two vector bundles on P
3. 相似文献
18.
E. Ballico 《Annali di Matematica Pura ed Applicata》2009,188(4):603-609
Here we study the totally arithmetically Cohen–Macaulay rank 2 vector bundles on any Hirzebruch surface F
e
.
E. Ballico was partially supported by MIUR and GNSAGA of INdAM (Italy). 相似文献
19.
Vincenzo Di Gennaro 《Geometriae Dedicata》1998,71(1):91-96
We exhibit a simpler and quick proof of a theorem proved by G. Ellingsrud and Ch. Peskine, which states that there are only a finite number of components in the Hilbert scheme parametrizing smooth surfaces in P4 not of general type. 相似文献
20.
A. S. Tikhomirov 《Acta Appl Math》2003,75(1-3):271-279
We study the moduli scheme M(2;0,n) of rank-2 stable vector bundles with Chern classes c
1=0, c
2=n, on the Fano threefold X – the double space P
3 of index two. New component of this scheme is produced via the Serre construction using certain families of curves on X. In particular, we show that the Abel–Jacobi map :HJ(X) of any irreducible component H of the Hilbert scheme of X containing smooth elliptic quintics on X into the intermediate Jacobian J(X) of X factors by Stein through the quasi-finite (probably birational) map g:M of (an open part of) a component M of the scheme M(2;0,3) to a translate of the theta-divisor of J(X). 相似文献