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} }
24 Citations
A DIVISION ALGORITHM IN AN AFFINE FRAMEWORK FOR FLAT FAMILIES COVERING HILBERT SCHEMES
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- 2012
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
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- 2018
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
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- 2015
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.
On the functoriality of marked families
- Mathematics
- 2013
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
- MathematicsJournal of Algebra
- 2020
Marked bases over quasi-stable modules
- Mathematics
- 2015
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
- Mathematics
- 2015
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
- Mathematics
- 2020
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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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…
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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…