Author | Chirka, E. M. author |
---|---|
Title | Complex Analytic Sets [electronic resource] / by E. M. Chirka |
Imprint | Dordrecht : Springer Netherlands, 1989 |
Connect to | http://dx.doi.org/10.1007/978-94-009-2366-9 |
Descript | XX, 372 p. online resource |
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. Stokesโ theorem -- A4.4. Fubiniโs 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