Determinantal Varieties Over Truncated Polynomial Rings
| dc.creator | Kosir, Tomaz | |
| dc.creator | Sethuraman, B. A. | |
| dc.date | 2002-12-03 | |
| dc.date.accessioned | 2026-07-07T04:53:31Z | |
| dc.date.available | 2026-07-07T04:53:31Z | |
| dc.description | We study higher order determinantal varieties obtained by considering generic $m\times n$ ($m \le n$) matrices over rings of the form $F[t]/(t^k)$, and for some fixed $r$, setting the coefficients of powers of $t$ of all $r \times r$ minors to zero. These varieties can be interpreted as generalized tangent bundles over the classical determinantal varieties; a special case of these varieties first appeared in a problem in commuting matrices. We show that when $r = m$, the varieties are irreducible, but when $r < m$, these varieties have at least $\lfloor {k/2}\rfloor + 1$ components. In fact, when $r=2$ (for any $k$), or when $k=2$ (for any $r$), there are exactly $\lfloor {k/2}\rfloor + 1$ components. We give formulas for the dimensions of these components in terms of $k$, $m$, and $n$. In the case of square matrices with $r=m$, we show that the ideals of our varieties are prime and that the coordinate rings are complete intersection rings, and we compute the degree of our varieties via the combinatorics of a suitable simplicial complex. | |
| dc.description | 29 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0212051 | |
| dc.identifier | http://arxiv.org/abs/math/0212051 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65878 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14M12 (Primary), 13P10 (Secondary) | |
| dc.title | Determinantal Varieties Over Truncated Polynomial Rings | |
| dc.type | text |