The geometry of A-graded algebras
| dc.creator | Sturmfels, Bernd | |
| dc.date | 1994-10-31 | |
| dc.date.accessioned | 2026-07-07T09:06:16Z | |
| dc.date.available | 2026-07-07T09:06:16Z | |
| dc.description | We study algebras k[x_1,...,x_n]/I which admit a grading by a subsemigroup of N^d such that every graded component is a one-dimensional k-vector space. V.I.~Arnold and coworkers proved that for d = 1 and n <= 3 there are only finitely many isomorphism types of such A-graded algebras, and in these cases I is an initial ideal (in the sense of Groebner bases) of a toric ideal. In this paper it is shown that Arnold's finiteness theorem does not extend to n = 4. Geometric conditions are given for I to be an initial ideal of a toric ideal. The varieties defined by A-graded algebras are characterized in terms of polyhedral subdivisions, and the distinct A-graded algebras are parametrized by a certain binomial scheme. | |
| dc.description | 16 pages, plain TEX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9410032 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9410032 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149948 | |
| dc.subject | Algebraic Geometry | |
| dc.title | The geometry of A-graded algebras | |
| dc.type | text |