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Structure of a neighbourhood of a complex compact submanifold in a complex manifold

Seria
Rozprawy Matematyczne tom/nr w serii: 219 wydano: 1983
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CONTENTS
Introduction...................................................................................................................................................................5
1. Notation and some definitions...................................................................................................................................6
  (a) Analytic families.....................................................................................................................................................6
  (b) Coordinate neighbourhoods and the normal bundle of a submanifold..................................................................7
  (c) A characteristic system for an analytic family.........................................................................................................9
  (d) Mutual positions of submanifolds.........................................................................................................................10
2. Sufficient conditions for triviality of the normal bundle.............................................................................................11
  (a) Formulations of the conditions.............................................................................................................................11
  (b) Connection of condition $(**)_{[U_i]}$ with the normal bundle.............................................................................12
  (c) Construction and some properties of functions $f_i$...........................................................................................14
  (d) Proof of triviality of the normal bundle.................................................................................................................16
  (e) Formulation of the results of Section 2................................................................................................................19
3. A maximum principle for 0-cochains of holomorphic functions on a connected compact complex manifold.............20
4. Construction of an analytic family............................................................................................................................21
  (a) Formulation of the main theorem.........................................................................................................................21
  (b) Construction of first coefficients of formal power series.......................................................................................23
  (c) Some lemmas......................................................................................................................................................25
  (d) The induction step - construction of the coefficients $φ_{i|ν+1}$........................................................................28
  (e) Proof of the convergence of the formal power series..........................................................................................31
  (0 Proof of the main theorem....................................................................................................................................33
Appendix....... .............................................................................................................................................................36
  (a) Formulation of sufficient conditions for the convergence of formal power series.................................................36
  (b) Some estimates...................................................................................................................................................38
  (c) Proof of Proposition A.1.......................................................................................................................................42
References.................................................................................................................................................................44
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 219
Liczba stron
44
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXIX
Daty
wydano
1983
Twórcy
Bibliografia
  • [1] R. Dwilewicz, Some properties of complex compact submanifolds, Bull. Acad. Polon. Sci. Sér. sci. math. astr. phys. 25 (1977), pp. 957-960.
  • [2] R. Dwilewicz, Completeness of characteristic systems for analytic families of compact submanifolds of a complex manifold (Polish), Thesis, Institute of Mathematics, Warsaw University.
  • [3] K. Kodaira, Some results in the transcendental theory of algebraic varieties, Ann. of Math. 59 (1954), pp. 86-134.
  • [4] K. Kodaira, Characteristic linear systems of complete continuous systems, Amer. J. Math. 78 (1956), pp. 716-744.
  • [5] K. Kodaira, A theorem of completeness of characteristic systems for analytic families of compact submanifolds of complex manifolds, Ann. of Math. 75 (1962), pp. 146-162.
  • [6] K. Kodaira, Collected Works, Iwanami Shoten, Publishers and Princeton University Press, 1975.
  • [7] K. Kodaira, J. Morrow, Complex manifolds, Holt, Rinehart and Winston, Inc., 1971.
  • [8] K. Kodaira, D. C. Spencer, On deformations of complex analytic structures, I, II, Ann. of Math. 67 (1958), pp. 328-466.
  • [9] K. Kodaira, D. C. Spencer, A theorem of completeness of characteristic systems of complete continuous systems, Amer. J. Math. 81 (1959), pp. 477-500.
  • [10] O. Zariski, Algebraic surfaces. Second supplemented edition, Springer-Verlag, Berlin-Heidelberg-New York 1971.
Języki publikacji
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Identyfikator YADDA
bwmeta1.element.zamlynska-2ba5e71c-cfcd-4625-b7a2-3b5915a2c10e
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ISBN
83-01-04357-1
ISSN
0012-3862
Kolekcja
DML-PL
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