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Ryotaro Hanyu

Publications and source records attributed to Ryotaro Hanyu.

2 recordsLinked to original sources
arXiv2026

Finiteness of the set of associated primes for local cohomology modules of ideals via properties of almost factorial rings

We investigate the finiteness of the set of associated primes for local cohomology modules $H_I^{i}(J)$ of an ideal $J$ generated by an $R$-sequence, through the comparison of $H_I^{d+1}(J)$ and $H_I^d(R/J)$, where $d = \mathrm{depth}_I(R)$. The properties of almost factorial rings play a key role in enabling this comparison. Under suitable conditions, we prove that the finiteness of $\mathrm{Ass} H_I^{d+1}(J)$ is equivalent to that of $\mathrm{Ass} H_I^d(R/J)$. Moreover, we give a few conditions under which the finiteness of $\mathrm{Ass} H_I^i(J)$ holds for all $i$.

math.AC↗
arXiv2026

Generators of the initial ideal of simplicial toric ideals

We describe a generating set for the initial ideal of simplicial toric ideals with respect to the graded reverse lexicographic order, using representations of elements of affine monoids as sums of irreducible elements. Although the resulting generating set is not necessarily minimal, we demonstrate, through an example, how one can obtain the reduced Gröbner basis from it. Moreover, we compare the maximal degree of the Gröbner basis and the Castelnuvo-Mumford regularity.

math.AC↗