Determinantal schemes and Buchsbaum-Rim sheaves
| dc.creator | Kreuzer, M. | |
| dc.creator | Migliore, J. C. | |
| dc.creator | Nagel, U. | |
| dc.creator | Peterson, C. | |
| dc.date | 1997-08-26 | |
| dc.date.accessioned | 2026-07-07T09:07:23Z | |
| dc.date.available | 2026-07-07T09:07:23Z | |
| dc.description | Let $ϕ$ be a generically surjective morphism between direct sums of line bundles on $\proj{n}$ and assume that the degeneracy locus, $X$, of $ϕ$ has the expected codimension. We call $B_ϕ = \ker ϕ$ a (first) Buchsbaum-Rim sheaf and we call $X$ a standard determinantal scheme. Viewing $ϕ$ as a matrix (after choosing bases), we say that $X$ is good if one can delete a generalized row from $ϕ$ 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 $S$. | |
| dc.description | 20 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9708021 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9708021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150352 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | Primary 14M12,14F05; Secondary 13D02, 14C20, 13C40 | |
| dc.title | Determinantal schemes and Buchsbaum-Rim sheaves | |
| dc.type | text |