Upgraded methods for the effective computation of marked schemes on a strongly stable ideal

@article{Bertone2013UpgradedMF,
  title={Upgraded methods for the effective computation of marked schemes on a strongly stable ideal},
  author={Cristina Bertone and Francesca Cioffi and Paolo Lella and Margherita Roggero},
  journal={J. Symb. Comput.},
  year={2013},
  volume={50},
  pages={263-290}
}
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24 Citations
Background Citations
11
Methods Citations
5
Results Citations
3

24 Citations

A DIVISION ALGORITHM IN AN AFFINE FRAMEWORK FOR FLAT FAMILIES COVERING HILBERT SCHEMES
We study the family of ideals i R = K(x1;:::;xn) whose quotients R=i share the same ane Hilbert polynomial and the same monomial K-vector basis, that we choose to be the sous-escalierN (j) of a…
An overview on marked bases and applications
The Hilbert scheme was introduced by Grothendieck in the 60s. One can simply think of the Hilbert scheme Hilbp(t) as a set containing all the saturated homogeneous ideals I in a certain polynomial…
Quasi-stable ideals and Borel-fixed ideals with a given Hilbert polynomial
  • Cristina Bertone
  • Mathematics
    Applicable Algebra in Engineering, Communication and Computing
  • 2015
TLDR
The key tool for the proof of both algorithms is the combinatorial structure of a quasi-stable ideal, in particular a special set of generators for the considered ideals, the Pommaret basis.
A Borel open cover of the Hilbert scheme
On the functoriality of marked families
The application of methods of computational algebra has recently introduced new tools for the study of Hilbert schemes. The key idea is to define flat families of ideals endowed with a scheme…
Computing Quot schemes via marked bases over quasi-stable modules
Term-ordering free involutive bases
Marked bases over quasi-stable modules
Let $K$ be a field of any characteristic, $A$ be a Noetherian $K$-algebra and consider the polynomial ring $A[x_0,\dots,x_n]$. The present paper deals with the definition of marked bases for free…
Double-generic initial ideal and Hilbert scheme
Following the approach in the book “Commutative Algebra”, by D. Eisenbud, where the author describes the generic initial ideal by means of a suitable total order on the terms of an exterior power, we…
The Gröbner fan of the Hilbert scheme
We give a notion of “combinatorial proximity” among strongly stable ideals in a given polynomial ring with a fixed Hilbert polynomial. We show that this notion guarantees “geometric proximity” of the…
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References

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