Eero Hyry
A Note on the Buchsbaum-Rim function of a parameter module.
Wed, 03/03/2010 - 16:01 — SomNambulAuthors: Eero Hyry, Futoshi Hayasaka
Subjects: Commutative Algebra
AbstractIn this article, we prove that the Buchsbaum-Rim function
$\ell_A(\S_{\nu+1}(F)/N^{\nu+1})$ of a parameter module $N$ in $F$ is bounded
above by $e(F/N) \binom{\nu+d+r-1}{d+r-1}$ for every integer $\nu \geq 0$.
Moreover, it turns out that the base ring $A$ is Cohen-Macaulay once the
equality holds for some integer $\nu$. As a direct consequence, we observe that
the first Buchsbaum-Rim coefficient $e_1(F/N)$ of a parameter module $N$ is
always non-positive.Jumping numbers and ordered tree structures on the dual graph.
Mon, 01/11/2010 - 16:01 — SomNambulAuthors: Eero Hyry, Tarmo Järvilehto
Subjects: Commutative Algebra
AbstractLet R be a two-dimensional regular local ring having an algebraically closed
residue field and let a be a complete ideal of finite colength in R. In this
article we investigate the jumping numbers of a by means of the dual graph of
the minimal log resolution of the pair (X,a). Our main result is a
combinatorial criterium for a positive rational number to be a jumping number.
In particular, we associate to each jumping number certain ordered tree
structures on the dual graph.
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