Notions of L 2 -Dolbeault cohomology with values in vector bundles on singular complex spaces / vorgelegt von Martin L. Sera. Wuppertal, 2015
Inhalt
- Contents
- 1 Introduction
- 2 Preliminaries
- 2.1 Proper modifications
- 2.2 Resolution of complex curves
- 2.3 Coherent analytic sheaves
- 2.4 Canonical sheaves on singular spaces
- 2.5 Monoidal transformations w. r. t. sheaves
- 2.6 Plurisubharmonic functions on complex spaces
- 3 Linear Spaces
- 3.1 Fibre spaces
- 3.2 Definition of linear spaces and preliminaries
- 3.3 Primary component of a linear space
- 3.4 Corank and Cohen-Macaulay linear spaces
- 3.5 Linear spaces of small corank
- 4 Proper Modifications of Sheaves
- 4.1 Torsion-free preimages of direct image sheaves
- 4.2 Direct images of torsion-free preimage sheaves
- 4.3 Proof of Theorem 4.1
- 4.4 Holomorphic n-forms on singular spaces
- 4.5 Non-analytic preimages and direct images
- 5 The Dolbeault Operator on Complex Spaces
- 5.1 Local version of the weak extension, def. of K_X(F)
- 5.2 The extensions d-bar_w,s and d-bar_s,w
- 5.3 L^2-extension theorem
- 6 L^2-Riemann-Roch for Singular Complex Curves
- 6.1 Local L^2-theory of complex curves
- 6.2 L^2-cohomology of compact complex curves
- 6.3 Singular metrics
- 6.4 Weakly holomorphic functions
- 6.5 Applications
- 7 Nakano Semi-positive Vector Bundles on Manifolds
- 7.1 Positivity for vector bundles
- 7.2 A-priori-estimates for the d-bar-operator
- 7.3 L^2-vanishing theorems on complete manifolds
- 8 The Relative Vanishing Theorem
- 8.1 Irreducible complex spaces
- 8.2 Vanishing theorems for torsion-free sheaves
- 8.3 Sheaves with torsion
- 9 Ideal Sheaves
- 9.1 Proper modifications of reduced ideal sheaves
- 9.2 Submanifolds of holomorphically convex manifolds
- 10 Fine Resolutions of K_X(S)
- Bibliography