Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determinantal schemes and Buchsbaum-Rim sheaves   Let $\phi$ be a generically surjective morphism between direct sums of line
bundles on $\proj{n}$ and assume that the degeneracy locus, $X$, of $\phi$ has
the expected codimension. We call $B_{\phi} = \ker \phi$ a (first)
Buchsbaum-Rim sheaf and we call $X$ a standard determinantal scheme. Viewing
$\phi$ as a matrix (after choosing bases), we say that $X$ is good if one can
delete a generalized row from $\phi$ and have the maximal minors of the
resulting submatrix define a scheme of the expected codimension. In this paper
we give several characterizations of good determinantal schemes. In particular,
it is shown that being a good determinantal scheme of codimension $r+1$ is
equivalent to being the zero-locus of a regular section of the dual of a first
Buchsbaum-Rim sheaf of rank $r+1$. It is also equivalent to being standard
determinantal and locally a complete intersection outside a subscheme $Y
\subset X$ of codimension $r+2$. Furthermore, for any good determinantal
subscheme $X$ of codimension $r+1$ there is a good determinantal subscheme $S$
codimension $r$ such that $X$ sits in $S$ in a nice way. This leads to several
generalizations of a theorem of Kreuzer. For example, we show that for a
zeroscheme $X$ in $\proj{3}$, being good determinantal is equivalent to the
existence of an arithmetically Cohen-Macaulay curve $S$, which is a local
complete intersection, such that $X$ is a subcanonical Cartier divisor on $S$.

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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org