Tetrahedral Curves
| dc.creator | Migliore, Juan C. | |
| dc.creator | Nagel, Uwe | |
| dc.date | 2004-07-16 | |
| dc.date.accessioned | 2026-07-07T05:10:25Z | |
| dc.date.available | 2026-07-07T05:10:25Z | |
| dc.description | A tetrahedral curve is a space curve whose defining ideal is an intersection of powers of monomial prime ideals of height two. It is supported on a tetrahedral configuration of lines. Schwartau described when certain such curves are ACM, namely he restricted to curves supported on a certain four of the six lines. We consider the general situation. We first show that starting with an arbitrary tetrahedral curve, there is a particular reduction that produces a smaller tetrahedral curve and preserves the even liaison class. We call the curves that are minimal with respect to this reduction S-minimal curves. Given a tetrahedral curve, we describe a simple algorithm (involving only integers) that computes the S-minimal curve of the corresponding even liaison class; in the process it determines if the original curve is arithmetically Cohen-Macaulay or not. We also describe the minimal free resolution of an S-minimal curve, using the theory of cellular resolutions. This resolution is always linear. This result allows us to classify the arithmetically Buchsbaum, non-ACM tetrahedral curves. More importantly, it allows us to conclude that an S-minimal curve is minimal in its even liaison class; that is, the whole even liaison class can be built up from the S-minimal curve. Finally, we show that there is a large set of S-minimal curves such that each curve corresponds to a smooth point of a component of the Hilbert scheme and that this component has the expected dimension. | |
| dc.description | 31 pages | |
| dc.identifier | https://arxiv.org/abs/math/0407298 | |
| dc.identifier | http://arxiv.org/abs/math/0407298 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71924 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 13D02; 13C40; 14M06; 14M07 | |
| dc.title | Tetrahedral Curves | |
| dc.type | text |