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}
}
A DIVISION ALGORITHM IN AN AFFINE FRAMEWORK FOR FLAT FAMILIES COVERING HILBERT SCHEMES
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  • 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.
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References

SHOWING 1-10 OF 50 REFERENCES
Flat families by strongly stable ideals and a generalization of Gröbner bases
Gröbner Bases and Hilbert Schemes. I
IDEALS WITH AN ASSIGNED INITIAL IDEAL
The stratum St(J,� ) (the homogeneous stratum Sth(J,� ) respectively) of a mono- mial ideal J in a polynomial ring R is the family of all (homogeneous) ideals of R whose initial ideal with respect to
Rational components of Hilbert schemes
The Gr\"obner stratum of a monomial ideal $\id{j}$ is an affine variety that parametrizes the family of all ideals having $\id{j}$ as initial ideal (with respect to a fixed term ordering). The
Ideals with an Assigned Initial Ideals
The stratum St(J,≺) (the homogeneous stratum Sth(J,≺) respectively) of a monomial ideal J in a polynomial ring R is the family of all (homogeneous) ideals of R whose initial ideal with respect to the
BOREL OPEN COVERING OF HILBERT SCHEMES
Let p(t) be an admissible Hilbert polynomial in P n of degree d and Gotzmann number r. It is well known that Hilb n(t) can be seen as a closed subscheme of the Grasmannian G(N,s), where N = ` n+r n ´
On border basis and Gröbner basis schemes
Hilbert schemes of zerodimensional ideals in a polynomial ring can be covered with suitable affine open subschemeswhose construction is achieved using border bases. Moreover, border bases have proved
The Gröbner Fan of an Ideal
The Hilbert schemes of locally Cohen-Macaulay curves in P^3 may after all be connected
Progress on the problem whether the Hilbert schemes of locally Cohen-Macaulay curves in projective 3 space are connected has been hampered by the lack of an answer to a question that was raised by
...
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