On Serre duality and envelopes of holomorphy
نویسندگان
چکیده
منابع مشابه
Serre Duality and Applications
We carefully develop the theory of Serre duality and dualizing sheaves. We differ from the approach in [12] in that the use of spectral sequences and the Yoneda pairing are emphasized to put the proofs in a more systematic framework. As applications of the theory, we discuss the RiemannRoch theorem for curves and Bott’s theorem in representation theory (following [8]) using the algebraic-geomet...
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Let Ω be a domain in C. We prove the following theorem. If the envelope of holomorphy of Ω is schlicht over Ω, then the envelope is in fact schlicht. We provide examples showing that the conclusion of the theorem does not hold in Cn, n > 2. Additionally, we show that the theorem cannot be generalized to provide information about domains in C whose envelopes are multiply sheeted.
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We introduce the generalized Serre functor S on a skeletally-small Hom-finite Krull-Schmidt triangulated category C. We prove that its domain Cr and range Cl are thick triangulated subcategories. Moreover, the subcategory Cr (resp. Cl) is the smallest additive subcategory containing all the objects in C which appears as the third term (resp. the first term) of some Aulsander-Reiten triangle in ...
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In this article we characterize the envelope of holomorphy for the algebra of bounded type holomorphic functions on Riemann domains over a Banach space in terms of the spectrum of the algebra. We prove that evaluations at points of the envelope are always continuous but we show an example of a balanced open subset of c0 where the extensions to the envelope are not necessarily of bounded type, a...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1967
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1967-0222341-9