𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the effective Nullstellensatz

✍ Scribed by Zbigniew Jelonek

Publisher
Springer-Verlag
Year
2005
Tongue
English
Weight
275 KB
Volume
162
Category
Article
ISSN
0020-9910

No coin nor oath required. For personal study only.

πŸ“œ SIMILAR VOLUMES

A Sparse Effective Nullstellensatz
A Sparse Effective Nullstellensatz
✍ Martı́n Sombra πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 182 KB

We present bounds for the sparseness in the Nullstellensatz. These bounds can give a much sharper characterization than degree bounds of the monomial structure of the polynomials in the Nullstellensatz in case that the input system is sparse. As a consequence we derive a degree bound which can subst

A generic effective Nullstellensatz
A generic effective Nullstellensatz
✍ Ravikiran Rajagopal; Lee C. Potter πŸ“‚ Article πŸ“… 2005 πŸ› Elsevier Science 🌐 English βš– 261 KB

Kollar's sharp effective Nullstellensatz, which is independent of the number of polynomials, is shown to be a generically pessimistic bound. A generic effective Nullstellensatz is proven. The generic bound is approximately inversely proportional to the number of polynomials; further, the bound is li

A geometric effective Nullstellensatz
A geometric effective Nullstellensatz
✍ Lawrence Ein; Robert Lazarsfeld πŸ“‚ Article πŸ“… 1999 πŸ› Springer-Verlag 🌐 English βš– 140 KB
A Combinatorial Proof of the Effective N
A Combinatorial Proof of the Effective Nullstellensatz
✍ Thomas W. DubΓ© πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 481 KB

Let \(I\) be an ideal in the affine multi-variate polynomial ring \(\mathcal{A}=K\left[x_{1}, \ldots, x_{n}\right]\). Beginning with the work of Brownawell, there has been renewed interest in recent years in using the degrees of polynomials which generate \(I\) to bound the degree \(D\) such that: