共查询到20条相似文献,搜索用时 0 毫秒
1.
Benjamin McKay 《Comptes Rendus Mathematique》2011,349(15-16):893-896
We classify holomorphic Cartan geometries on every compact complex surface which contains a rational curve. 相似文献
2.
Roman J. Dwilewicz 《Monatshefte für Mathematik》2013,169(2):145-160
In this paper we give a complete characterization of vector bundles of any dimension over complex tori in which the Hartogs–Bochner holomorphic extension phenomenon holds. Since holomorphic sections of line bundles over complex tori can be identified with theta functions, the results are formulated in terms of this class. 相似文献
3.
Makoto Masumoto 《Journal d'Analyse Mathématique》2016,129(1):69-90
Let T be the space of marked once-holed tori and Y0 be a Riemann surface with marked handle. We investigate geometric properties of the set Ta[Y0] of X ∈ T that allow holomorphic mappings of X into Y0. We also examine the set Tc[Y0] of marked once-holed tori conformally embedded into Y0. It turns out that Ta[Y0] and Tc[Y0] have several properties in common. Our basic tool is a new notion, called a handle condition. 相似文献
4.
In this paper we show that Cartan geometries can be studied via transitive Lie groupoids endowed with a special kind of vector-valued multiplicative 1-forms. This viewpoint leads us to a more general notion, that of Cartan bundle, which encompasses both Cartan geometries and G-structures. 相似文献
5.
Sorin Dumitrescu 《Monatshefte für Mathematik》2010,19(2):145-154
We study local automorphisms of holomorphic Cartan geometries. This leads to classification results for compact complex manifolds admitting holomorphic Cartan geometries. We prove that a compact Kähler Calabi–Yau manifold bearing a holomorphic Cartan geometry of algebraic type admits a finite unramified cover which is a complex torus. 相似文献
6.
We describe the Chern classes of holomorphic vector bundles on non-algebraic complex torus of dimension 2. 相似文献
7.
Let X be a compact connected Kähler manifold such that the holomorphic tangent bundle TX is numerically effective. A theorem of Demailly et al. (1994) [11] says that there is a finite unramified Galois covering M→X, a complex torus T, and a holomorphic surjective submersion f:M→T, such that the fibers of f are Fano manifolds with numerically effective tangent bundle. A conjecture of Campana and Peternell says that the fibers of f are rational and homogeneous. Assume that X admits a holomorphic Cartan geometry. We prove that the fibers of f are rational homogeneous varieties. We also prove that the holomorphic principal G-bundle over T given by f, where G is the group of all holomorphic automorphisms of a fiber, admits a flat holomorphic connection. 相似文献
8.
Rolf Farnsteiner 《Transactions of the American Mathematical Society》2004,356(10):4181-4236
This paper investigates varieties of tori and Cartan subalgebras of a finite-dimensional restricted Lie algebra , defined over an algebraically closed field of positive characteristic . We begin by showing that schemes of tori may be used as a tool to retrieve results by A. Premet on regular Cartan subalgebras. Moreover, they give rise to principal fibre bundles, whose structure groups coincide with the Weyl groups in case is the Lie algebra of a smooth group . For solvable Lie algebras, varieties of tori are full affine spaces, while simple Lie algebras of classical or Cartan type cannot have varieties of this type. In the final sections the quasi-projective variety of Cartan subalgebras of minimal dimension is shown to be irreducible of dimension , with Premet's regular Cartan subalgebras belonging to the regular locus.
9.
Mathematical Notes - 相似文献
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Let
be a smoothly bounded compact pseudoconvex complex manifold of finite type in the sense of D’Angelo such that the complex
structure of M extends smoothly up to bM. Let m be an arbitrary nonnegative integer. Let f be a function in H(M)∩ Hm(M), where Hm(M) is the Sobolev space of order m. Then f can be approximated by holomorphic functions on
in the Sobolev space Hm(M). Also, we get a holomorphic approximation theorem near a boundary point of finite type. 相似文献
14.
Igor Nikolaev 《Proceedings of the American Mathematical Society》2006,134(4):973-981
The ``noncommutative geometry' of complex algebraic curves is studied. As a first step, we clarify a morphism between elliptic curves, or complex tori, and -algebras , or noncommutative tori. The main result says that under the morphism, isomorphic elliptic curves map to the Morita equivalent noncommutative tori. Our approach is based on the rigidity of the length spectra of Riemann surfaces.
15.
Holomorphic projective structures on compact complex surfaces 总被引:2,自引:0,他引:2
16.
Jaume Llibre 《Journal of Difference Equations and Applications》2013,19(12):2059-2068
We study the set of minimal periods of holomorphic self-maps of one- and two-dimensional complex tori. In particular, we characterize when the set of minimal periods of such maps is finite. In fact, we have an algorithm for doing this characterization for holomorphic self-maps of an arbitrary dimensional complex torus. 相似文献
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E. Ballico 《Annali dell'Universita di Ferrara》2002,48(1):21-23
LetX be a smooth complex compact surface without non-constant meromorphic functions. Here we prove the existence of rank holomorphic
vector bundles onX containing exactly one rank one saturated subsheaf.
Sunto SiaX una superficie complessa compatta non singolare senza funzioni meromorfe non costanti. In questo lavoro si domstra cheX possiede molti fibrati olomorfi di rango 2 contenenti un unico fibrato in rette.相似文献
19.
ZHONG ChunPing School of Mathematical Sciences Xiamen University Xiamen China 《中国科学 数学(英文版)》2010,(2)
Let M be a complex n-dimensional manifold endowed with a strongly pseudoconvex complex Finsler metric F. Let M be a complex m-dimensional submanifold of M, which is endowed with the induced complex Finsler metric F. Let D be the complex Rund connection associated with (M, F). We prove that (a) the holomorphic curvature of the induced complex linear connection on (M, F) and the holomorphic curvature of the intrinsic complex Rund connection ~* on (M, F) coincide; (b) the holomorphic curvature of ~* does not exceed the holomorphic curvature of D; (c) (M, F) is totally geodesic in (M, F) if and only if a suitable contraction of the second fundamental form B(·, ·) of (M, F) vanishes, i.e., B(χ, ι) = 0. Our proofs are mainly based on the Gauss, Codazzi and Ricci equations for (M, F). 相似文献
20.
Aaron Zerhusen 《Periodica Mathematica Hungarica》2018,77(1):27-33
We consider holomorphic automorphisms of infinite dimensional complex Banach spaces. First we look at automorphisms with an attracting fixed point to construct Fatou–Bieberbach domains in Banach spaces. Second, we look tame sets in Banach spaces. Recall that a discrete set in X is tame if it can be mapped onto an arithmetic progression via an automorphism of X. We show that bounded discrete sets of Banach spaces allowing a Schauder basis are tame. In contrast, \(l_\infty \) has several bounded discrete sets which are not tame. 相似文献