Cristina Bertone

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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)
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