A family of ideals of minimal regularity and the Hilbert series of Cr(̂)
نویسنده
چکیده
For a simplicial subdivison of a region in R, we analyze the dimension of the vector space C k ( ) of C piecewise polynomial functions (splines) on of degree at most k. We nd an exact sequence which allows us to prove that the dimension series for splines given by Billera and Rose in [5] does indeed agree with the bounds on the dimension of the spline space given by Alfeld and Schumaker in [1], [2]. We give su cient conditions for the Alfeld-Schumaker bounds to be attained in all degrees, where is a two-dimensional simplicial complex. The conditions are satis ed by the class of complexes considered by Chui and Wang in [6], but also by a much broader class of complexes. Furthermore, for conditions which involve only local geometric data, this result is the strongest possible.
منابع مشابه
Topics on the Ratliff-Rush Closure of an Ideal
Introduction Let be a Noetherian ring with unity and be a regular ideal of , that is, contains a nonzerodivisor. Let . Then . The :union: of this family, , is an interesting ideal first studied by Ratliff and Rush in [15]. The Ratliff-Rush closure of is defined by . A regular ideal for which is called Ratliff-Rush ideal. The present paper, reviews some of the known prop...
متن کاملIDEALS WITH (d1, . . . , dm)-LINEAR QUOTIENTS
In this paper, we introduce the class of ideals with $(d_1,ldots,d_m)$-linear quotients generalizing the class of ideals with linear quotients. Under suitable conditions we control the numerical invariants of a minimal free resolution of ideals with $(d_1,ldots,d_m)$-linear quotients. In particular we show that their first module of syzygies is a componentwise linear module.
متن کاملArens regularity and derivations of Hilbert modules with the certain product
Let $A$ be a $C^*$-algebra and $E$ be a left Hilbert $A$-module. In this paper we define a product on $E$ that making it into a Banach algebra and show that under the certain conditions $E$ is Arens regular. We also study the relationship between derivations of $A$ and $E$.
متن کاملCastelnuovo-Mumford regularity of products of monomial ideals
Let $R=k[x_1,x_2,cdots, x_N]$ be a polynomial ring over a field $k$. We prove that for any positive integers $m, n$, $text{reg}(I^mJ^nK)leq mtext{reg}(I)+ntext{reg}(J)+text{reg}(K)$ if $I, J, Ksubseteq R$ are three monomial complete intersections ($I$, $J$, $K$ are not necessarily proper ideals of the polynomial ring $R$), and $I, J$ are of the form $(x_{i_1}^{a_1}, x_{i_2}^{a_2}, cdots, x_{i_l...
متن کاملAn upper bound for the regularity of powers of edge ideals
A recent result due to Ha and Van Tuyl proved that the Castelnuovo-Mumford regularity of the quotient ring $R/I(G)$ is at most matching number of $G$, denoted by match$(G)$. In this paper, we provide a generalization of this result for powers of edge ideals. More precisely, we show that for every graph $G$ and every $sgeq 1$, $${rm reg}( R/ I(G)^{s})leq (2s-1) |E(G)|^{s-1} {rm ma...
متن کامل