L 2 Holomorphic Sections of Bundles over Weakly Pseudoconvex Coverings

We show the existence of L ² holomorphic sections of invariant line bundles over normal coverings of pseudoconvex domains using a L ² generalization of Demailly's Weyl type formula.     

Holomorphic vector fields with totally degenerate zeroes

A zero set of a holomorphic vector field is totally degenerate, if the endomorphism of the conormal sheaf induced by the vector field is identically zero. By studying a class of foliations generalizing foliations of C^*-actions, we show that if a projective manifold admits a holomorphic vector field with a smooth totally degenerate zero component,then the manifold is stably birational to that component of the zero set.When the vector field has an isolated totally degenerate zero, we prove that the manifold is rational. This is a special case of Carrell's conjecture.     

一般Hopf曲面上的一类全纯线丛的上同调维数的计算公式

研究了具有任意基本群的非主Hopf流形上的全纯线丛．我们利用推广了Douady序列，利用群作用的方法，具体给出了一类具有非交换基本群的Hopf曲面上全纯线丛上同调维数的计算公式。     

全纯函数族的正规定则

Let f be a holomorphic function on a domain D Lontaiu in C, and let a be a finite complex number. We denote by -↑Ef/(a) = {z ∈ D : f(z) = a, ignoring multiplicity} the set of all distinct α-points of f. Let F be a family of holomorphic functions on D. If there exist three finite values a, b(≠ O,α) and c(≠ O) such that for every f ∈F, -↑Ef′/(0) Lontain in -↑Ef(α） and -↑Ef′ (b) Lontain in -↑Ef(c), then F is a normal family on D.     

Properties for a Class of Holomorphic Mapson Hilbert Space

Itiswell-knownthattheanalyticfunctionwithpositiverealpartintheunitdiscofthecomplexplaneplaysaveryimportantroleinthegeometrictheoryofcomplexvariablefunc-tions.Ithasbeenremarkablehowtoextendtheclassicalresultofthetheoryoffunctionstoabstractspacesinrecentyears[2].Inthisnotewedefineageneralizedhalf-planeinHilbertspaceandfindthebiholomorphicmapoftheunitballonHilbertspaceontothishalf-plane.Asacorollary,wegiveashortproofofaresultin[5].UsingtheaboveholomooorphicmapweobtainthedistortiontheoremandPick…     

一类第一 Betti数为奇数的曲面上的向量丛

本文得到一些有关一类第一Betti数为奇数的曲面上的全纯向量丛的结果,以及例外Hopf曲面上的集合IS2(X,0)的描述．     

关于全纯函数的正规定则

研究涉及微分多项式与公共值的全纯函数族的正规性问题.设F为区域D内的全纯函数族,n 1为任一正整数,b为有限常数,如果对F中任意两个函数f与g,fn(f-1)f′与gn(g-1)g′在D内都以b为公共值,则F在D内正规.此结果对亚纯函数不成立.     

全纯函数的正规族

本文证明了两个正规族定理,分别改进了张国明、孙伟和庞学诚的一个结果和徐焱的一个结果.     

Holomorphic map with unipotent Jacobian matrices in C3

We prove that the holomorphic unipotent Jacobian conjecture is valid when n = 3.     

Effective Isometric Embeddings for Certain Hermitian Holomorphic Line Bundles

We consider bihomogeneous polynomials on complex Euclidean spacesthat are positive outside the origin and obtain effective estimateson certain modifications needed to turn them into squares ofnorms of vector-valued polynomials on complex Euclidean space.The corresponding results for hypersurfaces in complex Euclideanspaces are also proved. The results can be considered as Hermitiananalogues of Hilbert's seventeenth problem on representing apositive definite quadratic form on Rⁿ as a sum of squares ofrational functions. They can also be regarded as effective estimateson the power of a Hermitian line bundle required for isometricprojective embedding. Further applications are discussed.     

Proper Holomorphic Maps from Domains in C2 with Transverse Circle Action

The authors consider proper holomorphic mappings between smoothly bounded pseudoconvex regions in complex 2-space,where the domain is of finite type and admits a transverse circle action.The main result is that the closure of each irreducible component of the branch locus of such a map intersects the boundary of the domain in the union of finitely many orbits of the group action.     

Holomorphic Almost-Periodic Functions

The present paper gives a survey of up-to-date results of holomorphic almost-periodic functions and mappings in one and several complex variables.     

Holomorphic Maps of Compact Generalized Hopf Manifolds

We investigate holomorphic maps between compact generalized Hopf manifolds (i.e., locally conformal Kähler manifolds with parallel Lee form). We show that they preserve the canonical foliations. Moreover, we study compact complex submanifolds of g.H. manifolds and holomorphic submersions from compact g.H. manifolds.     

Holomorphic invariant forms of a bounded domain

Given a complete ortho-normal system  = (0, 1, 2, . . .) of L2H(D), the space of holomorphic and absolutely square integrable functions in the bounded domain D of Cn, we construct a holomorphic imbedding ι : D →■(n, ∞), the complex infinite dimensional Grassmann manifold of rank n. It is known that in ■(n, ∞) there are n closed (μ, μ)-forms τμ (μ = 1, . . . , n) which are invariant under the holomorphic isometric automorphism of ■(n, ∞) and generate algebraically all the harmonic differential forms of ...     

Holomorphic Hermite functions and ellipses

In 1990 van Eijndhoven and Meyers introduced systems of holomorphic Hermite functions and reproducing kernel Hilbert spaces associated with the systems on the complex plane. Moreover they studied the relationship between the family of all their Hilbert spaces and a class of Gelfand–Shilov functions. After that, their systems of holomorphic Hermite functions have been applied to studying quantization on the complex plane, combinatorics, and etc. On the other hand, the author recently introduced systems of holomorphic Hermite functions associated with ellipses on the complex plane. The present paper shows that their systems of holomorphic Hermite functions are determined by some cases of ellipses, and that their reproducing kernel Hilbert spaces are some cases of the Segal–Bargmann spaces determined by the Bargmann-type transforms introduced by Sjöstrand.     

Proper Holomorphic Mappings Between Some Nonsmooth Domains

61. IntroductionLet DI, DZ be two bounded domains in C", a holomorphic mapping F: DI ~ DZ isproper if F--'(K) is compact whenever K is compact. It is Obvious that for every boUndeddomain in C", there always edests proper holomorphic self-mapping. However, given tabbounded domains DI, DZ in C", it does not seem easy to answer whether there ealsts properholomorphic mapping F: DI ~ D2. A main result obtained in recellt y6ars isTheorem 1.1.[1] Let Z (a) and Z (P) be two Generalized P…     

一类全纯映射的增长性

§ 1.　NotationsandFormulas　　Let(N ,dS2 N)beaHermitianmanifoldofdimensionn ,anddS2 NitsHermitianmertric.Let{e1～ ,Λen～}oftype (1 ,0 )tangentvectorsconstitutealocalunitaryframefieldinanopensetofM .Let{ω1 ,Λωn}betheunitarycoframewhichconsistsofncomplex valuedlineardifferen tialformsoftype (1 ,0 )suchthatdS2 N =ωαω-α. (1 )Hereandbelowthesummationconventionisused ,i.e .,therepeatedindexmeanssummation .LetBbethebundleofallunitaryframesofN .Thentheforms{ωα}areformsinB .Itiswellkn…     

Holomorphic flat projective structures on projective threefolds

Here we classify projective 3-folds with a holomorphic flat projective structure and Kodaira dimension 1 or 2.The author was partially supported by MURST and GNSAGA of CNR (Italy).     

Proper Holomorphic Maps from Domains in ?2 with Transverse Circle Action

The authors consider proper holomorphic mappings between smoothly bounded pseudoconvex regions in complex 2-space, where the domain is of finite type and admits a transverse circle action. The main result is that the closure of each irreducible component of the branch locus of such a map intersects the boundary of the domain in the union of finitely many orbits of the group action.