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Codimension and connectedness of degeneracy loci over local rings

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Abstract

We deduce results on the dimension and connectedness of degeneracy loci of maps of finite modules \(f:M\rightarrow N\) over a local noetherian ring \((A,\mathfrak {m})\). We show for instance that the expected determinantal bounds on the dimension of the t-th degeneracy locus of f hold if \(f\in \mathfrak {m}\mathrm{Hom}(M,N)\), and that this degeneracy locus is connected in the expected dimension provided \({\hat{A}}\) is a domain.

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Authors and Affiliations

  1. Fakultät für Mathematik der Ruhr-Universität, Universitätsstr. 150, Geb. NA 2/72, 44780, Bochum, Germany

    Hubert Flenner

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907-1395, USA

    Bernd Ulrich

Authors
  1. Hubert Flenner
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  2. Bernd Ulrich
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Correspondence to Hubert Flenner.

Additional information

This work began during visits of the authors at their home institutions. They are grateful for the hospitality and the financial support from the DFG Schwerpunkt “Globale Methoden der komplexen Analysis”. The second author was supported in part by the NSF.

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Flenner, H., Ulrich, B. Codimension and connectedness of degeneracy loci over local rings. Math. Z. 286, 723–740 (2017). https://doi.org/10.1007/s00209-016-1780-0

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  • DOI: https://doi.org/10.1007/s00209-016-1780-0

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