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Field name	Details
Dewey Class	515.94
Title	Complex Analytic Sets ([EBook]) / by E. M. Chirka.
Author	Chirka, Evgenii Mikhailovich
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : Springer Netherlands , 1989.
Physical Details	XX, 372 pages : online resource.
Series	Mathematics and its applications. Soviet series 0169-6378 ; ; 46
ISBN	9789400923669
Summary Note	One service mathematics has rendered the 'Et moi, .. " si j'avait so comment en revenir, human race. It has put common sense back je n'y semis point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. able to do something with it Eric T. Bell o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.:
Contents note	1 Fundamentals of the theory of analytic sets -- 1. Zeros of holomorphic functions -- 2. Definition and simplest properties of analytic sets. Sets of codimension 1 -- 3. Proper projections -- 4. Analytic covers -- 5. Decomposition into irreducible components and its consequences -- 6. One-dimensional analytic sets -- 7. Algebraic sets -- 2 Tangent cones and intersection theory -- 8. Tangent cones -- 9. Whitney cones -- 10. Multiplicities of holomorphic maps -- 11. Multiplicities of analytic sets -- 12. Intersection indices -- 3 Metrical properties of analytic sets -- 13. The fundamental form and volume forms -- 14. Integration over analytic sets -- 15. Lelong numbers and estimates from below -- 16. Holomorphic chains -- 17. Growth estimates of analytic sets -- 4 Analytic continuation and boundary properties -- 18. Removable singularities of analytic sets -- 19. Boundaries of analytic sets -- 20. Analytic continuation -- Appendix Elements of multi-dimensional complex analysis -- A1. Removable singularities of holomorphic functions -- A1.2. Plurisubharmonic functions -- A1.3. Holomorphic continuation along sections -- A1.4. Removable singularities of bounded functions -- A1.5. Removable singularities of continuous functions -- A2.1. Holomorphic maps -- A2.2. The implicit function theorem and the rank theorem -- A3. Projective spaces and Grassmannians -- A3.1. Abstract complex manifolds -- A3.5. Incidence manifolds and the ?-process -- A4. Complex differential forms -- A4.1. Exterior algebra -- A4.2. Differential forms -- A4.3. Integration of forms. Stokes’ theorem -- A4.4. Fubini’s theorem -- A4.5. Positive forms -- A5. Currents -- A5.1. Definitions. Positive currents -- A5.3. Regularization -- A5.4. The ??-problem and the jump theorem -- A6. Hausdorff measures -- A6.1. Definition and simplest properties -- A6.3. The Lemma concerning fibers -- A6.4. Sections and projections -- References -- References added in proof.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-94-009-2366-9
Links to Related Works	Subject References: Algebraic Geometry . Functions of a Complex Variable . Functions of complex variables . Mathematics . Several Complex Variables and Analytic Spaces . Authors: Chirka, Evgenii Mikhailovich . Chirka, Evgenii Mikhailovich . Corporate Authors: SpringerLink (Online service) . Series: Mathematics and its applications. Soviet series . Classification: 515.94 .

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Complex Analytic Sets

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