The Dolbeault complex in infinite dimensions I
Copyright policy )The Dolbeault complex in infinite dimensions I
In this paper we introduce certain basic notions concerning infinite dimensional complex manifolds, and prove that the Dolbeault cohomology groups of infinite dimensional projective spaces, with values in finite rank vector bundles, vanish. Some applications of such vanishing theorems are discussed; e.g., we classify vector bundles of finite rank over infinite dimensional projective spaces. Finally, we prove a sharp theorem on solving the inhomogeneous Cauchy–Riemann equations on affine spaces.
- Purdue University West Lafayette United States
- Purdue University System United States
Mathematics - Complex Variables, Applications of analytic spaces to physics and other areas of science, Cauchy-Riemann equations, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, Infinite-dimensional holomorphy, Functional Analysis (math.FA), Mathematics - Functional Analysis, Banach spaces, 32F15; 46G20, 32F15, \(\overline{\partial}\) equation, Dolbeault cohomology, FOS: Mathematics, Complex Variables (math.CV), \(\overline\partial\) and \(\overline\partial\)-Neumann operators, 46G20
Mathematics - Complex Variables, Applications of analytic spaces to physics and other areas of science, Cauchy-Riemann equations, \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs, Infinite-dimensional holomorphy, Functional Analysis (math.FA), Mathematics - Functional Analysis, Banach spaces, 32F15; 46G20, 32F15, \(\overline{\partial}\) equation, Dolbeault cohomology, FOS: Mathematics, Complex Variables (math.CV), \(\overline\partial\) and \(\overline\partial\)-Neumann operators, 46G20
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