Analytic Sets. Coherence of Ideal Sheaves

  • Hans Grauert
  • Reinhold Remmert
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 265)


Analytic sets are zero sets of holomorphic functions. Such sets were already considered in the nineteenth century — long before the notion of a complex space was coined — as the natural generalization of algebraic sets which are zero sets of polynomials. One reason to study analytic sets and not just systems of the type w1= f1(z1, ..., z m ), ..., w n = f n (z1, ..., z n ) is that quite often the implicit function theorem cannot be applied to solve a given set of holomorphic equations.


Prime Ideal Open Neighborhood Complex Space Fundamental Theorem Neighborhood Versus 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Hans Grauert
    • 1
  • Reinhold Remmert
    • 2
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenGermany
  2. 2.Mathematisches InstitutUniversität MünsterMünsterGermany

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