On the Depth of the Fiber Cone of Filtrations

Multiplicity and Cohen-Macaulayness of Fiber Cones of Good Filtrations

“…Using weak-(FC)-sequences of ideals in local rings, the author of [20] characterized the multiplicity and the CohenMacaulayness of F m (I ) in terms of minimal reductions of ideals. The results of [20] recovered some earlier results of Huneke and Sally [9], Shah [17,18] and Cortadellas and Zarzuela [4].…”

“…These problems have concerned many authors over the years. Using different approaches, the authors investigated the Cohen-Macaulayness and other properties of fiber cones F m (I ) and F J (F ) (see, for instance, [1][2][3][4][5][6][7]9,11,12,20]). Using weak-(FC)-sequences of ideals in local rings, the author of [20] characterized the multiplicity and the CohenMacaulayness of F m (I ) in terms of minimal reductions of ideals.…”

The equations of Rees algebras of equimultiple ideals of deviation one

“…Part of this work has been focused on ideals having small deviations as well as on the interplay between the reduction number and the relation type (see, just to mention a few of them, [12], [13], [14], [15], [23], [24], [26], [27]). The particular hypotheses and interests in this note owe much to the works of T. Cortadellas and S. Zarzuela in [3], W. Heinzer and M.-K. Kim in [7], S. Huckaba in [12] and [13], N.V. Trung in [23] and [24], and W.V. Vasconcelos in [26].…”

Sobre a fibra especial e o teorema de Risler-Teissier para filtrações

“…Além disso, sempre supomos que a fibra especial F(F) e o anel graduado associado G(F) sejam Cohen-Macaulay. Se a dimensão da fibra especialé Capítulo 4 -A Propriedade da fibra especial ser Gorenstein para o caso de filtrações 36 maior que zero, pelo [CZ,Lema 3.1], I n+1 ⊆ mI n para todo n ≥ 0 e então F(F) = G(F)/mG(F).…”

“…Por [CZ,Proposição 2.3(iii) e Teorema 2.8], temos a 1 I n−1 ∩ mI n = a 1 mI n−1 . Além disso, por [HM,Proposição 3.5], a 1é um elemento regular.…”