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It is well known that the Chern classes ci of a rank n vector bundle on P N , generated by global sections, are non-negative if i ≤ n and vanish otherwise. This paper deals with the following question: does the above result hold for the wider class of reflexive sheaves? We show that the Chern numbers ci with i ≥ 4 can be arbitrarily negative for reflexive… (More)
In this paper we obtain some explicit expressions for the Euler characteristic of a rank n coherent sheaf F on P N and of its twists F(t) as polynomials in the Chern classes c i (F), also giving algorithms for the computation. The employed methods use techniques of umbral calculus involving symmetric functions and Stirling numbers.
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)
In the last years many authors contributed to develop and implement algorithms on polynomial factorization and even if the situation evolved rapidly, there is still room for improvements and new points of view. We focus on absolute factorization of rationally irreducible polynomials with integer coefficients. For such polynomials, the best current algorithm… (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 a paper in 2008, Herzog, Hibi and Ohsugi introduced and studied the semigroup ring associated to the set of minimal vertex covers of an unmixed bipartite graph. In this paper we relate the dimension of this semigroup ring to the rank of the Boolean lattice associated to the graph.
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)