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Residual intersections are Koszul–Fitting ideals

Part of: Commutative algebra: Homological methods Local rings and semilocal rings Special varieties Theory of modules and ideals Cycles and subschemes

Published online by Cambridge University Press:  23 September 2019

Vinicius Bouça  and
S. Hamid Hassanzadeh
Vinicius Bouça
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Brazil email bouca.vinicius@gmail.com, vbouca@im.ufrj.br
S. Hamid Hassanzadeh
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Brazil email hamid@im.ufrj.br, hassanzadeh.ufrj@gmail.com
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Abstract

We describe generators of disguised residual intersections in any commutative Noetherian ring. It is shown that, over Cohen–Macaulay rings, the disguised residual intersections and algebraic residual intersections are the same, for ideals with sliding depth. This coincidence provides structural results for algebraic residual intersections in a quite general setting. It is shown how the DG-algebra structure of Koszul homologies affects the determination of generators of residual intersections. It is shown that the Buchsbaum–Eisenbud family of complexes can be derived from the Koszul–Čech spectral sequence. This interpretation of Buchsbaum–Eisenbud families has a crucial rule to establish the above results.

Keywords

residual intersectionsFitting idealsKitt idealsresidual approximation complexessliding depthdisguised residual intersection

MSC classification

Primary: 13C40: Linkage, complete intersections and determinantal ideals 13D02: Syzygies, resolutions, complexes
Secondary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) 14C17: Intersection theory, characteristic classes, intersection multiplicities 14M06: Linkage
Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 11 , November 2019 , pp. 2150 - 2179
Copyright
© The Authors 2019 

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Footnotes

The first author was partially supported by PhD scholarships from CAPES-Brazil and from FAPERJ-Brazil. The second author was partially supported by the grant ‘bolsa de produtividade 301407/2016-9’ from CNPq-Brazil.

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