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Residual intersections
and the annihilator of Koszul homologies
Seyed Hamid Hassanzadeh and Jose Naéliton |
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Vol. 10 (2016), No. 4, 737–770
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DOI: 10.2140/ant.2016.10.737
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Abstract |
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We study Cohen–Macaulayness, unmixedness, the structure of the canonical module and the stability of the Hilbert function of algebraic residual intersections. We establish some conjectures about these properties for large classes of residual intersections without restricting the local number of generators of the ideals involved. To determine the above properties, we construct a family of approximation complexes for residual intersections. Moreover, we determine some general properties of the symmetric powers of quotient ideals which were not known even for special ideals with a small number of generators. Finally, we show acyclicity of a prime case of these complexes to be equivalent to finding a common annihilator for higher Koszul homologies, which unveils a tight relation between residual intersections and the uniform annihilator of positive Koszul homologies, shedding some light on their structure. |
Keywords
residual intersection, canonical module, type, sliding
depth, approximation complex, Koszul annihilator
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Mathematical Subject Classification 2010
Primary: 13C40
Secondary: 13H10, 13D02, 14C17, 14M06
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Milestones
Received: 21 January 2015
Revised: 13 January 2016
Accepted: 22 March 2016
Published: 20 June 2016
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Authors |
| Seyed Hamid Hassanzadeh | |
| Instituto de Matemática Universidade Federal do Rio de Janeiro Av. Athos da Silveira Ramos 149 Centro de Tecnologia - Bloco C Cidade Universitária - Ilha do Fundão 68530 21941-909 Rio de Janeiro Brazil |
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| Jose Naéliton | |
| Departamento de Matemática CCEN, Campus I - sn - Cidade Universitária Universidade Federal de Paraíba 58051-090 João Pessoa Brazil |
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