The analytic spread of codimension two monomial varieties

Gimenez, Philippe; Morales, Marcel; Simis, Aron

doi:10.1007/bf03322816

Cited by 4 publications

(5 citation statements)

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“…Furthermore I is normally torsion free, if and only if I is a complete intersection locally in codimension 3. We recall the definition, as in [8].…”

Section: Serre Properties Of R and Gmentioning

confidence: 99%

On the Depth of the Associated Graded Ring of an Ideal

Ghezzi

2002

Journal of Algebra

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Let R be a local Cohen᎐Macaulay ring, let I be an R-ideal, and let G be the associated graded ring of I. We give an estimate for the depth of G when G fails to be Cohen᎐Macaulay. We assume that I has a small reduction number and sufficiently good residual intersection properties and satisfies local conditions on the depth of some powers. The main theorem unifies and generalizes several known results. We also give conditions that imply the Serre properties of the Ž .blow-up rings. ᮊ 2002 Elsevier Science USA

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“…Furthermore I is normally torsion free, if and only if I is a complete intersection locally in codimension 3. We recall the definition, as in [8].…”

Section: Serre Properties Of R and Gmentioning

confidence: 99%

On the Depth of the Associated Graded Ring of an Ideal

Ghezzi

2002

Journal of Algebra

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“…In Morales (1995) it was proved that in the simplicial case I is generated by the 2 × 2 minors of a 2 × n matrix. A similar, more restricted, condition was proved in the general lattice case by Gimenez et al (1999). The quadratic relations come from the Plücker relations of some specials 2 × 4 matrices.…”

Section: Quadratic Relationsmentioning

confidence: 77%

“…The proofs developed here are new and different from those in Morales and Simis (1992), Gimenez et al (1999), and Barile and Morales (1998).…”

Section: Introductionmentioning

confidence: 90%

“…Here "simplicial" means that a subset of variables in is a system of parameters of the ring /I . For codimension 2 simplicial toric ideals, the fiber cone was completely described in Morales and Simis (1992), Gimenez et al (1999), Barile and Morales (1998), by hard computations from the explicit system of generators for I given in Morales (1995). However, the methods developed in these articles cannot be applied to the general case of toric ideals.…”

Section: Introductionmentioning

confidence: 99%

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Fiber Cone of Codimension 2 Lattice Ideals

Morales

2009

Communications in Algebra

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x 1 x 2 x r be a codimension two lattice ideal. In this article we study the arithmetic properties of the blow-up of the ideal I in . Let I = n≥0 I n / I n be the Fiber cone of I, we prove thatIn addition, if is infinite and I is radical, noncomplete intersection, then:• I has dimension 3, is reduced, arithmetically Cohen-Macaulay, of minimal degree. Moreover, a presentation of I is effective from the minimal system of generators of I. • An explicit minimal reduction of I is given. • The blow-up ring, or Rees ring I = n≥0 I n , is arithmetically Cohen-Macaulay and has a presentation by linear and quadratic forms. This article completes and extends to the general case of codimension 2 lattice ideals previous results for the simplicial toric case by Morales and Simis (1992), Gimenez et al. (1999), and Barile and Morales (1998).

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“…A particular class of varieties, of important interest in classical Geometry are Cohen-Macaulay varieties of minimal degree, they were classified geometrically by the successive contribution of Del Pezzo (1885) [DP], Bertini (1907) [B], and Xambo (1981) [X] and algebraically in Barile and Morales (2000) [BM2]. They appear naturally studying the fiber cone of a codimension two toric ideals Morales (1995) [M], Gimenez et al (1993Gimenez et al ( , 1999 [GMS1,GMS2], Barile and Morales (1998) [BM1], Ha (2006) [H], Ha and Morales (2009) [HM].…”

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confidence: 99%