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Two-sided bounds for canonical traces of Veronese subalgebras
Sora Miyashita
The classical Veronese formula of Goto--Watanabe identifies the canonical module of a Veronese subalgebra with the corresponding Veronese module. We prove the analogous compatibili…
Algebras with straightening laws on join- or meet-semidistributive lattices
Koji Matsushita, Sora Miyashita, Koichiro Tani
We study algebras with straightening laws on join- or meet-semidistributive lattices. We show that for a join-semidistributive (resp. meet-semidistributive) lattice, meet-distribut…
Canonical traces of Artinian truncations of Stanley-Reisner rings
Sora Miyashita
For a simplicial complex and integers , set . We give an exact combinatorial formula fo…
A Fitting criterion for quasi-Gorenstein local rings
Sora Miyashita
We prove that a Noetherian local ring with canonical module is quasi-Gorenstein if and only if $\Fitt_1^R(ω_R) \cong ω_R$. This settles the expectation of Eisenbud, Ficar…
Trace ideals of exterior powers of the module of differentials
Ryo Ishizuka, Sora Miyashita
For each , we study the trace ideal of the -th exterior power of the module of differentials. In characteristic zero, we show that these ideals characterize the polyno…
Higher-dimensional Teter rings via the canonical trace
Sora Miyashita, Taiga Ozaki
We study Puthenpurakal's higher-dimensional Teter rings via the canonical trace ideal. We give a sufficient criterion for Teterness and show that, in the standard graded case, it i…
Canonical traces of graded fiber products: applications to disconnected Stanley--Reisner rings
Shinya Kumashiro, Sora Miyashita
Recent work by Miyashita and Varbaro classified the canonical traces of Stanley--Reisner rings that are Gorenstein on the punctured spectrum, under the Cohen--Macaulay assumption.…
When do pseudo-Gorenstein rings become Gorenstein?
Sora Miyashita
We discuss the relationship between the trace ideal of the canonical module and pseudo-Gorensteinness. In particular, under certain mild assumptions, we show that every pseudo-Gore…
The canonical trace of Stanley-Reisner rings that are Gorenstein on the punctured spectrum
Sora Miyashita, Matteo Varbaro
In this paper we prove that nearly Gorenstein Stanley-Reisner rings of dimension at least 3 are indeed Gorenstein. By previous work of the first author this yields a complete chara…
A linear generalization of the nearly Gorenstein property, with applications to Veronese subalgebras
Sora Miyashita
We studies the nearly Gorenstein property for Veronese subalgebras of (semi-)standard graded algebras. We introduce a condition~ for Cohen--Macaulay semi-standard grade…
Conditions of multiplicity and applications for almost Gorenstein graded rings
Koji Matsushita, Sora Miyashita
In this paper, we prove that if Cohen-Macaulay local/graded rings , and satisfy certain conditions regarding multiplicity and Cohen-Macaulay type, then almost Gorens…
Comparing generalized Gorenstein properties in semi-standard graded rings
Sora Miyashita
Semi-standard graded rings are a generalized notion of standard graded rings. In this paper, we compare generalized notions of the Gorenstein property in semi-standard graded rings…
Nearly Gorenstein projective monomial curves of small codimension
Sora Miyashita
In this paper, we characterize nearly Gorenstein projective monomial curves of codimension 2 and 3.
Levelness versus nearly Gorensteinness of homogeneous domains
Sora Miyashita
Levelness and nearly Gorensteinness are well-studied properties of graded rings as a generalized notion of Gorensteinness. In this paper, we compare the strength of these propertie…