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Upgraded methods for the effective computation of marked schemes on a strongly stable ideal. Abstract. Let J ⊂ S = K[x0,. .. , xn] be a monomial strongly stable ideal. The collection Mf(J) of the homogeneous polynomial ideals I, such that the monomials outside J form a K-vector basis of S/I, is called a J-marked family. It can be endowed with a structure of… (More)

Let p(t) be an admissible Hilbert polynomial in P n of degree d. The Hilbert scheme Hilb n p(t) can be realized as a closed subscheme of a suitable Grassmannian G, hence it could be globally defined by homogeneous equations in the Plücker coordinates of G and covered by open subsets given by the non-vanishing of a Plücker coordinate, each embedded as a… (More)

Let f (X, Y) ∈ Z[X, Y ] be an irreducible polynomial over Q. We give a Las Vegas absolute irreducibility test based on a property of the Newton polytope of f , or more precisely, of f modulo some prime integer p. The same idea of choosing a p satisfying some prescribed properties together with LLL is used to provide a new strategy for absolute factorization… (More)

The present paper investigates properties of quasi-stable ideals and of Borel-fixed ideals in a polynomial ring $$k[x_0,\dots ,x_n]$$ k [ x 0 , ⋯ , x n ] , in order to design two algorithms: the first one takes as input n and an admissible Hilbert polynomial P(z), and outputs the complete list of saturated quasi-stable ideals in the chosen polynomial ring… (More)

In this paper, we present a modular strategy which describes key properties of the absolute primary decomposition of an equidimensional polynomial ideal defined by polynomials with rational coefficients. The algorithm we design is based on the classical technique of elimination of variables and colon ideals and uses a tricky choice of prime integers to work… (More)

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