Mixed Buchsbaum--Rim Multiplicities
| dc.creator | Kleiman, Steven | |
| dc.creator | Thorup, Anders | |
| dc.date | 1994-12-20 | |
| dc.date | 1995-08-18 | |
| dc.date.accessioned | 2026-07-07T08:57:55Z | |
| dc.date.available | 2026-07-07T08:57:55Z | |
| dc.description | We prove the results about mixed Buchsbaum--Rim multiplicities announced in (9.10)(ii) on p.224 of our recent paper [J.Alg.(1994)], including a general mixed-multiplicity formula. In addition, we identify these multiplicities as the coefficients of the ``leading form'' of the appropriate Buchsbaum-Rim polynomial in three variables, and we prove a positivity theorem. In fact, we define the multiplicities as the degrees of certain zero-dimensional ``mixed twisted'' Segre classes, and we develop an encompassing general theory of these new rational equivalence classes in all dimensions. In parallel, we develop a theory of pure ``twisted'' Segre classes, and we recover the main results in [J.Alg.(1994)] about the pure Buchsbaum--Rim multiplicities, the polar multiplicities, and so forth. Moreover, we identify the additivity theorem [J.Alg.(1994), (6.7b)(i), p.205] as giving a sort of residual-intersection formula, and we show its (somewhat unexpected) connection to the mixed-multiplicity formula. Also, we work in a more general setup than before, and we develop a new approach, based on the completed normal cone. | |
| dc.description | AmS-TeX-Ver 2.1 with amsppt.sty-ver 2.1c. The introduction was made more readable, and a number of minor correction were made. Hard copies are available on request | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9412019 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9412019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147119 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14C17, 14B05, 13D40, 13H15 | |
| dc.title | Mixed Buchsbaum--Rim Multiplicities | |
| dc.type | text |