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- W2377084497 abstract "Let R = K[X1, . . . , Xn;Y1, . . . , Ym] be a polynomial ring in two sets of variables. Let r, k ≥ 1 be integers, then Ir,s is the Veronese-type ideal generated on degree r by the set {X1 1 . . . X ain n | ∑n j=1 aij = r, 0 ≤ aij ≤ s, s ∈ {1, . . . , r}} and Jk,s is the Veronese-type ideal generated on degree k by the set {Y bi1 1 . . . Y bim m | ∑m j=1 bij = k, 0 ≤ bij ≤ s, s ∈ {1, . . . , k}}. In [10] the author introduced the Veronese bi-type ideals Lq,s = ∑ r+k=q Ir,sJk,s generated in the same degree q. For s = 2 the Veronese bi-type ideals are the ideals of the walks of a bipartite graph with loops. In [9] the author studies the combinatorics of the integral closure and the normality of Lq,2. More in general, in [10] the same problem is studied for Lq,s for all s. In this paper we are interested to study the symmetric algebra of these classes of monomial ideals. In order to compute the standard invariants we investigate in which cases these monomial ideals are generated by s-sequences. In [6] the notion of s-sequences has been employed to compute the invariants of the symmetric algebra of finitely generated modules. The proposal is to compute standard invariants of the symmetric algebra in terms of the corresponding invariants of special quotients of the ring R. This computation can be obtained for finitely generated R-modules generated by an s-sequence. In Section 1 we consider the ideals of Veronese-type Iq,s. We give the conditions such that Iq,s is generated by an s-sequence. Then we compute standard algebraic invariants of the symmetric algebra of Iq,s." @default.
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- W2377084497 date "2010-01-01" @default.
- W2377084497 modified "2023-09-27" @default.
- W2377084497 title "ON A CLASS OF MONOMIAL IDEALS GENERATED BY s-SEQUENCES" @default.
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