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A generalized Gaeta’s theorem

Part of: Theory of modules and ideals Special varieties

Published online by Cambridge University Press:  01 May 2008

Elisa Gorla
Elisa Gorla*
Affiliation:
Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland (email: elisa.gorla@math.unizh.ch)
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Abstract

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We generalize Gaeta’s theorem to the family of determinantal schemes. In other words, we show that the schemes defined by minors of a fixed size of a matrix with polynomial entries belong to the same G-biliaison class of a complete intersection whenever they have maximal possible codimension, given the size of the matrix and of the minors that define them.

Keywords

determinantal schemeG-biliaisongeneralized divisorgenerically complete intersection schemecomplete intersection

MSC classification

Secondary: 14M06: Linkage 14M12: Determinantal varieties 14M10: Complete intersections 13C40: Linkage, complete intersections and determinantal ideals
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 3 , May 2008 , pp. 689 - 704
Copyright
Copyright © Foundation Compositio Mathematica 2008

References

The author was partially supported by the Swiss National Science Foundation under grant no. 107887. Part of the research in this paper was done while the author was a guest at the Max Planck Institut für Mathematik in Bonn. The author would like to thank the Max Planck Institute for its support and hospitality.