StronglyStableIdeals
Macaulay2 package StronglyStableIdeals -- Find strongly stable ideals with a given Hilbert polynomial. Strongly stable ideals are a key tool in commutative algebra and algebraic geometry. These ideals have nice combinatorial properties that make them well suited for both theoretical and computational applications. In the case of polynomial rings with coefficients in a field of characteristic zero, the notion of strongly stable ideals coincides with the notion of Borel-fixed ideals. Borel-fixed ideals are fixed by the action of the Borel subgroup of triangular matrices and a famous result by Galligo says that generic initial ideals are of this type. In the context of Hilbert schemes, Galligo’s theorem means that each component and each intersection of components contains at least a point corresponding to a scheme defined by a Borel-fixed ideal. Hence, these ideals are distributed throughout the Hilbert schemes and they can be used to understand its local structure. The main feature of the this package is a method to compute the set of all saturated strongly stable ideals in a given polynomial ring with a given Hilbert polynomial
Keywords for this software
References in zbMATH (referenced in 11 articles , 2 standard articles )
Showing results 1 to 11 of 11.
Sorted by year (- Bertone, Cristina; Cioffi, Francesca; Roggero, Margherita: Smoothable Gorenstein points via marked schemes and double-generic initial ideals (2022)
- Fröberg, Ralf; Nicklasson, Lisa: Gorenstein rings generated by strongly stable sets of quadratic monomials (2022)
- Ceria, Michela: Combinatorial decompositions for monomial ideals (2021)
- Kambe, Yuta; Lella, Paolo: The Gröbner fan of the Hilbert scheme (2021)
- Ceria, Michela: Bar code for monomial ideals (2019)
- Lella, Paolo: Strongly stable ideals and Hilbert polynomials (2019)
- Bertone, Cristina; Cioffi, Francesca; Roggero, Margherita: Double-generic initial ideal and Hilbert scheme (2017)
- Bertone, Cristina: Quasi-stable ideals and Borel-fixed ideals with a given Hilbert polynomial (2015)
- Cioffi, F.; Di Gennaro, R.: When the positivity of the (h)-vector implies the Cohen-Macaulay property (2014)
- Lella, Paolo: An efficient implementation of the algorithm computing the Borel-fixed points of a Hilbert scheme (2012)
- Cioffi, Francesca; Lella, Paolo; Marinari, Maria Grazia; Roggero, Margherita: Segments and Hilbert schemes of points (2011)