Let X be a geometrically connected smooth projective curve of genus one, defined over the field of real numbers, such that X does not have any real points. We classify the isomorphism classes of all stable real algebraic vector bundles over X .

Abstract In this paper, we establish the Kobayashi–Hitchin correspondence, that is, equivalence of existence an Einstein–Hermitian metric and $\psi $-polystability a generalized holomorphic vector bundle over compact Kähler manifold symplectic type. Poisson modules provide intriguing bundles, obtain $-stable complex surfaces are not stable in ordinary sense.

If X is a connected, finite CJF-complex, we can define iKO)~iX) to be [X, BO] (base-point preserving homotopy classes of maps). Recall [2] that if xEiKO)~iX), the geometrical dimension of x (abbreviated g.dim x) can be defined to be the smallest nonnegative integer k such that a representative of x factors through BO(k). If $ is a vector bundle over X, the class in (PO)~(X) of a classifying map...

Let X be a smooth curve of genus g. For any vector bundles E , F on X , let μE,F : H 0(X, E) ⊗ H 0(X, F) → H 0(X, E ⊗ F) be the multiplication map. Here we study the injectivity of μE,F when E , F are general stable bundles with h1(X, E) = h1(X, F) = 0.

Let X be a smooth projective curve of genus g ≥ 2 defined over an algebraically closed field k of characteristic p > 0. For p sufficiently large (explicitly given in terms of r, g) we construct an atlas for the locus of all Frobenius-destabilized bundles (i.e. we construct all Frobenius-destabilized bundles of degree zero up to isomorphism). This is done by exhibiting a surjective morphism from...

We show how the weight of automorphic forms is related to the holomorphic positive and negative line bundles. Then, from the relation of holomorphic vector bundles and the existence of Yang-Mills connection on the stable bundle , we discuss how the weight of automorphic forms can be associated with the transition function of the Yang-Mills connection.

We show that the locus of stable rank four vector bundles without theta divisor over a smooth projective curve of genus two is in canonical bijection with the set of theta-characteristics. We give several descriptions of these bundles and compute the degree of the rational theta map.

We develop a semistability algorithm for vector bundles which are given as a kernel of a surjective morphism between splitting bundles on the projective space P over an algebraically closed field K. This class of bundles is a generalization of syzygy bundles. We show how to implement this algorithm in a computer algebra system. Further we give applications, mainly concerning the computation of ...