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Titlebook: Several Complex Variables VII; Sheaf-Theoretical Me H. Grauert,Th. Peternell,R. Remmert Book 1994 Springer-Verlag Berlin Heidelberg 1994 Co

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书目名称Several Complex Variables VII
副标题Sheaf-Theoretical Me
编辑H. Grauert,Th. Peternell,R. Remmert
视频video
丛书名称Encyclopaedia of Mathematical Sciences
图书封面Titlebook: Several Complex Variables VII; Sheaf-Theoretical Me H. Grauert,Th. Peternell,R. Remmert Book 1994 Springer-Verlag Berlin Heidelberg 1994 Co
描述Of making many books there is no end; and much study is a weariness of the flesh. Eccl. 12.12. 1. In the beginning Riemann created the surfaces. The periods of integrals of abelian differentials on a compact surface of genus 9 immediately attach a g­ dimensional complex torus to X. If 9 ~ 2, the moduli space of X depends on 3g - 3 complex parameters. Thus problems in one complex variable lead, from the very beginning, to studies in several complex variables. Complex tori and moduli spaces are complex manifolds, i.e. Hausdorff spaces with local complex coordinates Z 1, ... , Zn; holomorphic functions are, locally, those functions which are holomorphic in these coordinates. th In the second half of the 19 century, classical algebraic geometry was born in Italy. The objects are sets of common zeros of polynomials. Such sets are of finite dimension, but may have singularities forming a closed subset of lower dimension; outside of the singular locus these zero sets are complex manifolds.
出版日期Book 1994
关键词Complex analysis; Complex spaces; Kohomologie; Kohärente Garben; Konvexität und Konkavität; Modifikation;
版次1
doihttps://doi.org/10.1007/978-3-662-09873-8
isbn_softcover978-3-642-08150-7
isbn_ebook978-3-662-09873-8Series ISSN 0938-0396
issn_series 0938-0396
copyrightSpringer-Verlag Berlin Heidelberg 1994
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Pseudoconvexity, the Levi Problem and Vanishing Theorems, not arbitrary but satisfies a certain condition of pseudoconvexity. The question whether conversely such a pseudoconvex domain is a domain of holomorphy became famous as the so-called “Levi problem” and influenced the development of complex analysis over several decades. The Levi problem was first
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Theory of ,-Convexity and ,-Concavity,domains in the complex number space ℂ.. Section 2 carries over the results to complex spaces and to arbitrary coherent analytic sheaves, proves extension theorems and introduces the Fréchet topology in the set of local cross sections. In § 3 the finiteness of the dimension of cohomology vector space
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Modifications,romorphic equivalence. Roughly speaking, two complex spaces .,. are bimeromorphically equivalent if they are isomorphic outside thin analytic sets. If . and . are irreducible, this means that their fields of meromorphic functions are isomorphic. For two given spaces . and . which are bimeromorphical
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Introduction,e very beginning, to studies in . complex variables. Complex tori and moduli spaces are complex manifolds, i.e. Hausdorff spaces with local complex coordinates z.,..., z.; holomorphic functions are, locally, those functions which are holomorphic in these coordinates.
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Theory of ,-Convexity and ,-Concavity,ion theorems and introduces the Fréchet topology in the set of local cross sections. In § 3 the finiteness of the dimension of cohomology vector spaces is proved in certain cases. Section 4 gives some applications: When can a hole in a complex space be filled. When do hulls for cohomology classes exist and when does the cohomology vanish?
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