Ample vector bundles with zero loci of sectional genus two

Let X be a smooth complex projective variety and let be a smooth submanifold of dimension , which is the zero locus of a section of an ample vector bundle of rank on X. Let H be an ample line bundle on X, whose restriction H_Z to Z is generated by global sections. Triplets as above are classified under the assumption that is a polarized manifold of sectional genus 2. This can be regarded as a step towards the classification of ample vector bundles of corank one and curve genus two. Received: 6 June 2003     

Discriminant loci of ample and spanned line bundles

Let (X,L,V) be a triplet where X is an irreducible smooth complex projective variety, L is an ample and spanned line bundle on X and V⊆H⁰(X,L) spans L. The discriminant locus D(X,V)⊂|V| is the algebraic subset of singular elements of |V|. We study the components of D(X,V) in connection with the jumping sets of (X,V), generalizing the classical biduality theorem. We also deal with the degree of the discriminant (codegree of (X,L,V)) giving some bounds on it and classifying curves and surfaces of codegree 2 and 3. We exclude the possibility for the codegree to be 1. Significant examples are provided.     

Slice modules over minimal 2-fundamental algebras

We consider a class of algebras whose Auslander-Reiten quivers have starting components that are not generalized standard. For these components we introduce a generalization of a slice and show that only in finitely many cases (up to isomorphism) a slice module is a tilting module. The first named author was supported by the Polish Scientific Grant KBN No 1 P03A 018 27     

一类量子Koszul代数的${\mathbb{Z}}_{2}$-Galois 覆盖的 Hochschild上同调

考虑一类量子Koszul代数的 ${\mathbb{Z}}_{2}$-Galois覆盖$\Lambda_{\q}$, 并计算 这类代数的各阶Hochschild上同调群的维数, 进而利用道路的语言, 刻画了 Hochschild上同调环的cup积. 作为应用, 给出了这类代数的Hochschild上同调环模掉幂零理想的 代数结构.     

Stability of rank 2 vector bundles along isomonodromic deformations

We are interested in the stability of holomorphic rank 2 vector bundles of degree 0 over compact Riemann surfaces, which are provided with irreducible meromophic tracefree connections. In the case of a logarithmic connection on the Riemann sphere, such a vector bundle will be trivial up to the isomonodromic deformation associated to a small move of the poles, according to a result of A. Bolibruch. In the general case of meromorphic connections over Riemann surfaces of arbitrary genus, we prove that the vector bundle will be semi-stable, up to a small isomonodromic deformation. More precisely, the vector bundle underlying the universal isomonodromic deformation is generically semi-stable along the deformation, and even maximally stable. For curves of genus g ≥ 2, this result is non-trivial even in the case of non-singular connections. The author was partially supported by ANR SYMPLEXE BLAN06-3-137237.     

Gr?bner–Shirshov Basis of Derived Hall Algebra of Type A_n

We know that in Ringel–Hall algebra of Dynkin type, the set of all skew commutator relations between the iso-classes of indecomposable modules forms a minimal Gr?bner–Shirshov basis,and the corresponding irreducible elements forms a PBW type basis of the Ringel–Hall algebra. We aim to generalize this result to the derived Hall algebra DH(A_n) of type A_n. First, we compute all skew commutator relations between the iso-classes of indecomposable objects in the bounded derived category D~b(A_n) using the Auslander–Reiten quiver of D~b(A_n), and then we prove that all possible compositions between these skew commutator relations are trivial. As an application, we give a PBW type basis of DH(A_n).     

Ample vector bundles with zero loci having a bielliptic curve section of low degree

Let be an ample vector bundle of rank r ≥ 2 on a smooth complex projective variety X of dimension n such that there exists a global section of whose zero locus Z is a smooth subvariety of dimension n − r ≥ 3 of X. Let H be an ample line bundle on X such that its restriction H _Z to Z is very ample. Triplets are classified under the assumption that (Z,H _Z ) has a smooth bielliptic curve section of genus ≥ 3 with .      

On stable and ample vector bundles of rank 2 on curves

Ohne Zusammenfassung     

量子外代数的Galois覆盖代数的Hochschild上同调

本文研究一类量子代数$\Lambda^n_q$的Hochschild上同调.量子代数$\Lambda^n_q$的极小投射双模分解被构造, $\Lambda^n_q$的各阶Hochschild上同调群的维数被清晰的给出.此外,对一些特殊的情况, $\Lambda^n_q$的上同调环也被清晰的刻画.     

Globally generated vector bundles of rank 2 on a smooth quadric threefold

We investigate the existence of globally generated vector bundles of rank 2 with _c1≤3$c_1\le 3$ on a smooth quadric threefold and determine their Chern classes. As an automatic consequence, every rank 2 globally generated vector bundle on Q$Q$ with _c1=3$c_1=3$ is an odd instanton up to twist.     

The moduli spaces of rank 2 stable vector bundles over Veronesean surfaces

Partially supported by DGICYT PB88-0224     

Moduli of rank 4 symplectic vector bundles over a curve of genus 2

Let X be a complex projective curve which is smooth and irreducibleof genus 2. The moduli space ₂ of semistable symplectic vectorbundles of rank 4 over X is a variety of dimension 10. Afterassembling some results on vector bundles of rank 2 and odddegree over X, we construct a generically finite cover of ₂by a family of 5-dimensional projective spaces, and outlinesome applications.     

Ample and spanned vector bundles of top Chern number two on smooth projective varieties

The purpose of this paper is to classify ample and spanned vector bundles of top Chern number two on smooth projective varieties of arbitrary dimension defined over an algebraically closed field of characteristic zero.

     

On the classification of complex vector bundles of stable rank

One describes, using a detailed analysis of Atiyah-Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This classification becomes more effective on generalized flag manifolds, where the Lie algebra formalism and concrete integrability conditions describe in constructive terms the Chern classes of a vector bundle. Since deceased.     

Kirkman packing and covering designs with spanned holes of size 2

A Kirkman holey packing (resp. covering) design, denoted by KHPD(g^u) (resp. KHCD(g^u)), is a resolvable (gu, 3, 1) packing (resp. covering) design of pairs with u disjoint holes of size g, which has the maximum (resp. minimum) possible number of parallel classes. Each parallel class contains one block of size δ, while other blocks have size 3. Here δ is equal to 2, 3, and 4 when gu ≡ 2, 3, and 4 (mod 3) in turn. In this paper, the existence problem of a KHPD(2^u) and a KHCD(2^u) is solved with one possible exception of a KHPD(2⁸). © 2004 Wiley Periodicals, Inc.     

The Structure of Weak Hopf Algebras Corresponding to U q (sl 2)

The structure of weak Hopf algebras corresponding to U _q (sl ₂) are classified by their algebra structure and coalgebra structure. The algebra structure of weak Hopf algebras corresponding to U _q (sl ₂) can be written as the direct sum of U _q (sl ₂) and an algebra of polynomials. The coalgebra structure of weak Hopf algebras corresponding to U _q (sl ₂) are classified by their Ext quiver. There are four types of such structures.