Showing papers on "Frame bundle published in 1989"
TL;DR: In this article, the authors consider the space of flat connections on the trivial SU(2) bundle over a surface M, modulo the space for gauge transformations and prove that if the surfaceM is now endowed with a complex structure, this line bundle is isomorphic to the determinant bundle.
Abstract: Following M. F. Atiyah and R. Bott [AB] and E. Witten [W], we consider the space of flat connections on the trivialSU(2) bundle over a surfaceM, modulo the space of gauge transformations. We describe on this quotient space a natural hermitian line-bundle with connection and prove that if the surfaceM is now endowed with a complex structure, this line bundle is isomorphic to the determinant bundle. We show heuristically how path-integral quantisation of the Chern-Simons action yields holomorphic sections of this bundle.
138 citations
TL;DR: In this article, it was shown that a vector bundle E on a grassmannian (resp. on a quadric) splits as a direct sum of line bundles if and only if certain cohomology groups involving E and the quotient bundle are zero.
Abstract: In this paper we prove that a vector bundle E on a grassmannian (resp. on a quadric) splits as a direct sum of line bundles if and only if certain cohomology groups involving E and the quotient bundle (resp. the spinor bundle) are zero. When rank E=2 a better criterion is obtained considering only finitely many suitably chosen cohomology groups.
90 citations
TL;DR: NarNarasimhan and Ramanathan as discussed by the authors described a different construction of the moduli space generalising the method of Gieseker, which is much simpler and shorter than in [2].
Abstract: Seshadri introduced the notion of parabolic structures on vector bundles [4] and later constructed a moduli space for semistable parabolic vector bundles on curves [2]. In this small note we describe a different construction of the moduli space generalising the method of Gieseker [1]. This has some advantages. This construction is much simpler and shorter than in [2]. It avoids the use of unitary bundles and hence is applicable in positive characteristics. One does not need the introduction and comparison of different parabolic structures. Moreover, some computations which have to be repeated here (proposition 2) become simpler in this method. The generalisation to parabolic principal bundles will be considered in a subsequent paper. I would like to thank M. S. Narasimhan and A. Ramanathan for helpful discussions.
39 citations
TL;DR: In this paper, the authors use a form of Whitehead's concept of crossed module, in place of the idea of an abstract kernel, to find an obstruction class in ǫ 2(B,ZG) (G the fibre-type of M) whose vanishing gives a necessary and sufficient condition for the existence of such a Lie group bundle isomorphic to M.
35 citations
TL;DR: For a twisted spin bundle corresponding to a flat Hermitian vector bundle, the associated twistor-spinors admit the same conformal invariants as for a spin manifold as mentioned in this paper.
Abstract: Two interesting conformal invariants which are constant on the manifold are given for twistor-spinors on a spin manifold following the notion of a twistor-spinor associated to a twisted spin bundle. For a twisted spin bundle corresponding to a flat Hermitian vector bundle, the associated twistor-spinors admit the same conformal invariants.
34 citations
01 Dec 1989
TL;DR: In this article, the authors construct a line bundle on a complex projective manifold (a general ruled variety over a curve) which is not ample, but whose restriction to every proper subvariety is ample.
Abstract: We construct a line bundle on a complex projective manifold (a general ruled variety over a curve) which is not ample, but whose restriction to every proper subvariety is ample. This example is of interest in connection with ampleness questions of vector bundles on varieties of dimension greater than one. The method of construction shows that a stable bundle of positive degree on a curve is ample. The example can be used to show that there is no restriction theorem for Bogomolov stability.
20 citations
01 Jan 1989
TL;DR: In this article, the authors present an agreement between the Université de Lyon and the Publications du Département de mathématiques de Lyon, which implique l'accord avec les conditions générales d'utilisation.
Abstract: © Université de Lyon, 1989, tous droits réservés. L’accès aux archives de la série « Publications du Département de mathématiques de Lyon » implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
14 citations
TL;DR: In this paper, a complex connected projective nonsingular algebraic surface endowed with an ample line bundle L, which is spanned by its global sections, is considered, and pairs with sectional genus g(X, L) with g(L·(K X ⊗L))/2=3 are classified by means of the main techniques of adjunction theory.
Abstract: Let X be a complex connected projective nonsingular algebraic surface endowed with an ample line bundle L, which is spanned by its global sections. Pairs (X, L) as above, with sectional genus g(X, L)=1+(L·(K X ⊗L))/2=3 are classified by means of the main techniques of adjunction theory.
11 citations
TL;DR: On the normal bundle of a submanifold in a Riemannian space, a natural Riemanian metric is introduced in this paper, and the structure of surfaces with strongly parabolic normal bundle metric is determined.
Abstract: On the normal bundle of a submanifold in a Riemannian space a natural Riemannian metric is introduced. The structure of surfaces with strongly parabolic normal bundle metric is determined. It is shown that the Sasaki metric of the normal bundle of vectors of fixed length of a two-dimensional Veronese surface has constant sectional curvature.Bibliography: 16 titles.
10 citations
01 Aug 1989
TL;DR: In this article, the canonical line bundle and the Hodge bundle over moduli spaces for low genus was studied and a natural measure on the moduli space of every genus which is related to the Siegel symplectic metric on Siegel upper half-space as well as to Hodge metric on Hodge bundles was given.
Abstract: We study some explicit relations between the canonical line bundle and the Hodge bundle over moduli spaces for low genus This leads to a natural measure on the moduli space of every genus which is related to the Siegel symplectic metric on Siegel upper half-space as well as to the Hodge metric on the Hodge bundle
TL;DR: In this paper, the existence of a connection on a super vector bundle or on a principal super fibre bundle is equivalent to the vanishing of a cohomological invariant of the superbundle.
Abstract: We show that the existence of a connection on a super vector bundle or on a principal super fibre bundle is equivalent to the vanishing of a cohomological invariant of the superbundle. This invariant is proved to vanish in the case of a De Witt base supermanifold. Finally, some examples are discussed.
TL;DR: With the help of Weil polynomials on the Lie algebra of the Poincare group in D dimensions, the authors constructed a Lagrangian form for higher dimensional gravity on a principal fibre bundle whose base space is an even-dimensional Riemann-Cartan spacetime and whose structure group is the PoINCare group.
TL;DR: In this article, the behavior of holomorphic vector bundles with supplementary curvature conditions was studied and it was shown that a global holomorphic section of a holomorphic Hermitian bundle with positive curvature and compact base has a nonempty set of zeros.
Abstract: We study the behavior of holomorphic vector bundles with supplementary curvature conditions. Let L ~ M be a holomorphic line or bundle on the complex manifold M and g be a fibrewise Hermitian metric of positive curvature on L. Then (as follows easily from [i, p. 170]) the function g(7, ~) has no relative minima for any everywhere nonzero section ~ ~ H ° (M~ ~ (L)). Generalizing this fact, S. Kobayashi noted [2, p. 166] that a global holomorphic section of a holomorphic Hermitian bundle with positive curvature and compact base has a nonempty set of zeros (the outline of the corresponding argument is given in [2]). Unfortunately, the latter is not always true (cf. the example below). Kobayashi's remark is valid under an additional restriction.
TL;DR: In this article, an upper bound for the order of a stable vector bundle α over X in terms of the dimension of X and order of the characteristic classes of α is derived.
TL;DR: In this paper, a new formalism is introduced to define conformal connections on a vector bundle, endowed with a conformal class of pseudo-riemannian metrics of signature (p, q).