Cohomological dimension of certain algebraic varieties

DOI10.1090/S0002-9939-02-06500-0zbMath0998.13007OpenAlexW1880264126MaRDI QIDQ4547026

Massoud Tousi, Kamran Divaani-Aazar, Reza Naghipour

Publication date: 20 August 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-02-06500-0

zbMATH Keywords

cohomological dimensioncanonical moduleconnectedness dimensionsubdimension

Mathematics Subject Classification ID

Homological dimension and commutative rings (13D05) Local cohomology and commutative rings (13D45) Local cohomology and algebraic geometry (14B15) Higher-dimensional local connectedness (54F35)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A vanishing theorem for local cohomology modules
• On the vanishing of local cohomology modules
• Some basic results on canonical modules
• On the endomorphism ring of the canonical module
• Some theorems about formal functions
• Cohomological dimension of algebraic varieties
• Ideal topologies, local cohomology and connectedness
• Über lokale Kohomologiegruppen hoher Ordnung.

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