# On The Type Of Associated Graded Ring Of Certain Monomial Curves

Patil, DP and Tamone, G (2002) On The Type Of Associated Graded Ring Of Certain Monomial Curves. In: Communications in Algebra, 30 (11). pp. 5181-5198.

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## Abstract

Let p,m,d be positive integers, $m_i$ := m + id, 0 \leq i \leq p and let n be positive integer such that gcd(m,d,n) = 1 and m_0 < n. Let A be the coordinate ring of the algebroid monomial curve in the affine algebroid (p + 2) -space $A_k ^{p+2}$ over a field K, defined parametrically by $X_1 = T^{m_0}, X_2 = T^{m_1}, ....., X_p = T^{m_p}, X_{p+1}$ = $T^n$. In this article assuming that the associated graded ring $gr_m(A)$of A is Cohen-Maucaulay (and some more mild additional assumptions, see(2.4), we give ana explicit formula for the type of $gr_m(A)$ in terms of the standard basis of the semigroup generated by the almost arithmetic progression $m_0,m_1,....,m_p$,n. Our special assumptions are satisfied if p = 1, that is, for the class of algebroid monomial space curves.

Item Type: Journal Article Copyright of this article belongs to Taylor & Francis. Division of Physical & Mathematical Sciences > Mathematics 21 Jul 2008 19 Sep 2010 04:47 http://eprints.iisc.ernet.in/id/eprint/15137