The analytic spread of the ideal of a monomial curve in projective 3-space

Simplicial ideals, 2-linear ideals and arithmetical rank

“…Our results apply to the special case where X is the fiber cone proj F(I L ) of a lattice ideal I L of codimension two. Let recall that by the succesively works [G], [GMS1], [GMS2], [BM1] and [HM], the fiber cone is a reduced arithmetically Cohen-Macaulay algebraic set of minimal degree. See section 4.…”

“…Throughout this paper we will work with projective schemes X ⊂ IP r , but we adopt the algebraic point of view, that is we consider a polynomial ring S, graded by its standard graduation and reduced homogeneous ideals. Our motivation comes from the study of the fiber cone F (I) of a codimension two toric ideal, as it was shown in [GMS1], [GMS2],…”

“…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].…”