Sagbi bases with applications to blow-up algebras.
Sagbi bases with applications to blow-up algebras.
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Sagbi 基础及其在爆炸代数中的应用。
DOI：
10.1515/crll.1996.474.113
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
G. Valla
中科院分区：
文献类型：
--
作者：
A. Conca;J. Herzog;G. Valla
are Cohen-Macaulay or normal and they are able to decide whether I is of linear type. Successively, they consider the class of ideals I ( c, d ) generated by the two minors of a matrix of the form ( x 1 . . . x i . . . x c x d +1 x d + i . . x c + d ) which define certain rational normal scrolls. They prove that the natural generators of the Rees algebra and special fiber of I ( c, d ) form a SAGBI-basis, they compute the relations of these algebras and show that they are Cohen-Macaulay normal domains and have rational singularities. Moreover, they are able to prove that the analytic spread of the defining ideal of any rational normal curve in P n is n + 1 , whenever n ≥ 4 . Finally, they study numerical data of the special fiber of R ( I ) (where I = I ( c, d ) , as above). They show that the initial ideal of the defining ideal of the special fiber is an ideal of square-free monomials (for a suitable term-order). They show that the attached simplicial complex is shellable and that the Hilbert function is obtained by determining the h -vectors of the algebra. In particular, this allows to determine those fibers which are Gorenstein.
