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 |

SUMMARY

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 nonยญ 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 nonยญ 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 comยญ 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

CONTENT

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{128}{153} theorem -- A4.4. Fubiniโ{128}{153}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

Mathematics
Algebraic geometry
Functions of complex variables
Mathematics
Several Complex Variables and Analytic Spaces
Algebraic Geometry
Functions of a Complex Variable