Complex Analysis: Lectures given at a Summer School of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Bressanone (Bolzano), Italy, June 3-12, 1973 (C.I.M.E. Summer Schools, 62)

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NINE LECTURES ON COMPLES ANALYSIS
	Preface
	CONTENTS
	Chapter 1. Elementary theory of holomorohic convexity
		1.1 Preliminaries
		1.2 Hartogs domains
		1.3 Open seta of holomorphy
		1.4 Levi (1)-convexity
		Exerclses
	Chapter II. Pseudoconcave manifolds
		2.1 Preliminaries
		2.2. Mermorohic functions and holomorphic line bundles
		2.3 Pseudoconcave manifolds
		2.4. Analytic and algebraic dspendence of meromorphic functions
		2.5. Algebraic fields of meromorphic functions
	Chapter III. Properly discontinuous pseudoconcave groups:the Siegel modular group
		3.1. Preliminaries
		3.2. Pauedoconcave properlY discontinuous groups
		3.3 Siegel modular group
		3.4 Pseudoconcavity of the modular group
		3.5. Poincare series
	Chapter IV. Projective imbeddings of Dseudoconcave manifolds
		4.1. Measure of pseudoconcavity
		4.2 The problem of projective imbedding of pseudoconcave manifolds
		4.3 Solution of the problem for o-pseudoconcave .manifolds
		4.4. The case of dimE X >=3.
	Chapter V:. Meromorphic functions on complex spaces
		5.1 Preliminaries
		5.2 Pseudoconcavity for complex spaces
		5.3 The Poincare problem
		5.4. Relative theorems
	Chapter VI: .E. E. Levi problem.
		6.1 Preliminaries.
		6.2 E.E. Levi problem
		6.3 Proof of Grauert\'s theorem
		6.4. Characterization of projective algebraic manifolds,Kodaira\'s theorem
	Chapter VII:. Generalizations of the Levi-problem
		7.1. d-open sets of holomorphy
		7.2. Proof of theorem (Grauert)
		7.3 Finiteness theorems
		7.4 Applications to projective algebraic manifolds
	Chapter VIII. Duality theorems on complex manifolds
		8.1 Preliminaries.
		8.2. Cech homology on complex manifolds
		8.3. Duality between cohomology and homology
		8.4. Cech homology and the functor EXT
		8.5 Divisors and Riemann-Roch theorem
	Chapter IX. The H. Lewy problem
		9.1. Preliminaries
		9.2. Mayer-Vietrois sequence
		9.3. Bochner theorem
		9.4. Riemann-Hilbert and Cauchy problem
		9.5. Cauchy-problem as a Vanishing theorem for cohomology
		9.6. Non-validity of Poincare lemma for the complex
	BIBLIOGRAPHY
PROPAGATION OF SINGULARITIESFOR THE CAUCHY. RIEMANN EQUATIONS
	Introduction
	Leoture 1. The a- problem and Hartog\'s theorem
	Lecture 2. Pseudo-convexity
	Lecture 3. Pormulation of the a-Neumann problem
	Lecture 4. The bastc a prtort esttmates
	Lecture 5. Pseudo-differential operators
	Lecture 6. Interlor regularlty and exlstence theorems
	Lecture 7. Boundary regularity
	Lecture 8. The 1nduced Cauchy-Rlemann equat10ns
	References
THE MIXED CASE OF THE DIRECT IMAGETHEOREM AND ITS APPLICATIONS
	THB MIXED CASE OF THE DIRECT IMAGE THEOREMAND ITS APPLICATIONS
	§ 0. Introduction
	Table of Contents
	PART I: CONSTRUCTION OF SlMPLEXES OF BANACH BUNDLES
		§l Privileged Polydiscs
		§2 Semi-norms on Unreduced Spaces
		§3.Theorem B with Bounds
		§4. Leray\'s Theorem with Bounds
		§5. Extension of Cohomology Classes
		§6. Sheaf Systems
	PART II THE POWER SERIES METHOD
		§7 Finite Generation with fuunds
		§8. Right Inverses of Coboundary Maps
		§9. Global Isomorphism
		§10. Proof of Coherence
	PART III: APPLICATIONS
		§11. Coherent Sheaf Extension
		§12. Blow-downs
		§13. Relative Exceptional Sets
		§14. Projectivity Criterion
		§15. Extension of Complex Spaces
	APPENDIX
	REFERENCES