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

Roman Dwilewicz. Structure of a neighbourhood of a complex compact submanifold in a complex manifold. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1983. <http://eudml.org/doc/268648>.

@book{RomanDwilewicz1983,
abstract = {CONTENTSIntroduction...................................................................................................................................................................51. 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.........................................................................................................................102. 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................................................................................................................193. A maximum principle for 0-cochains of holomorphic functions on a connected compact complex manifold.............204. 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....................................................................................................................................33Appendix....... .............................................................................................................................................................36  (a) Formulation of sufficient conditions for the convergence of formal power series.................................................36  (b) Some estimates...................................................................................................................................................38  (c) Proof of Proposition A.1.......................................................................................................................................42References.................................................................................................................................................................44},
author = {Roman Dwilewicz},
keywords = {existence of holomorphic mapping of neighbourhood of submanifold; compact complex submanifold},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Structure of a neighbourhood of a complex compact submanifold in a complex manifold},
url = {http://eudml.org/doc/268648},
year = {1983},
}

TY - BOOK
AU - Roman Dwilewicz
TI - Structure of a neighbourhood of a complex compact submanifold in a complex manifold
PY - 1983
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSIntroduction...................................................................................................................................................................51. 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.........................................................................................................................102. 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................................................................................................................193. A maximum principle for 0-cochains of holomorphic functions on a connected compact complex manifold.............204. 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....................................................................................................................................33Appendix....... .............................................................................................................................................................36  (a) Formulation of sufficient conditions for the convergence of formal power series.................................................36  (b) Some estimates...................................................................................................................................................38  (c) Proof of Proposition A.1.......................................................................................................................................42References.................................................................................................................................................................44
LA - eng
KW - existence of holomorphic mapping of neighbourhood of submanifold; compact complex submanifold
UR - http://eudml.org/doc/268648
ER -