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Codimension and connectedness of degeneracy loci over local rings

Hubert Flenner·Bernd Ulrich
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Abstract

We deduce results on the dimension and connectedness of degeneracy loci of maps of finite modules $f:M\to N$ 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 $f\in {\mathfrak m} Hom (M,N)$, and that this degeneracy locus is connected in the expected dimension provided $\hat A$ is a domain.

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Hubert Flenner, Bernd Ulrich. 2005-06-06. Codimension and connectedness of degeneracy loci over local rings. https://arxiv.org/abs/math/0506095

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