Vol. 10, No. 4, 2016

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Residual intersections and the annihilator of Koszul homologies

Seyed Hamid Hassanzadeh and Jose Naéliton

Vol. 10 (2016), No. 4, 737–770
DOI: 10.2140/ant.2016.10.737
Abstract

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
Mathematical Subject Classification 2010
Primary: 13C40
Secondary: 13H10, 13D02, 14C17, 14M06
Milestones
Received: 21 January 2015
Revised: 13 January 2016
Accepted: 22 March 2016
Published: 20 June 2016
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
Jose Naéliton
Departamento de Matemática
CCEN, Campus I - sn - Cidade Universitária
Universidade Federal de Paraíba
58051-090 João Pessoa
Brazil