Related papers: Gorenstein Simplices and Even Binary Self-Compleme…
We prove that a finite dimensional algebra $A$ with representation-finite subcategory consisting of modules that are semi-Gorenstein-projective and $n$-th syzygy modules is left weakly Gorenstein. This generalises a theorem of Ringel and…
We study the algebras of modular forms on type IV symmetric domains for simple lattices; that is, lattices for which every Heegner divisor occurs as the divisor of a Borcherds product. For every simple lattice $L$ of signature $(n,2)$ with…
This article concerns commutative algebras over a field $k$ of characteristic zero which are finite dimensional as vectorspaces, and particularly those of such algebras which are graded. Here the term graded is applied to non-negatively…
We investigate nearly Gorenstein property for a normal graded ring $R = \bigoplus_{n\ge 0}R_n$ finitely generated over a field. For that purpose, we investigate ${K_R}^{-1}$, the inverse of $K_R$ (the canonical module of $R$) and introduce…
We present a classification of all weighted projective spaces with at worst terminal or canonical singularities in dimension four. As a corollary we also classify all four-dimensional one-point lattice simplices up to equivalence. Finally,…
We give conditions on when a triangular matrix ring is Gorenstein of a given selfinjective dimension. We apply the result to the category algebra of a finite EI category. In particular, we prove that for a finite EI category, its category…
For a commutative Gorenstein Noetherian ring $R$, we construct an affine scheme $X$ solely from DG singularity category $S_{dg}(R)$ of $R$ such that there is a finite surjective morphism $X \rightarrow \mathrm{Spec}(R /I)$, where…
There is given a characterization for the Rees algebras of parameters in a Gorenstein local ring to be almost Gorenstein graded rings. A characterization is also given for the Rees algebras of socle ideals of parameters. The latter one…
The main message of the paper is that for Gorenstein singularities, whose (real) link is rational homology sphere, the Artin--Laufer program can be continued. Here we give the complete answer in the case of elliptic singularities. The main…
We introduce pseudo-Gorenstein rings and characterize those Hibi rings attached to a finite distributive lattice L which are pseudo-Gorenstein. The characterization is given in terms of the poset of join-irreducible elements of L. We also…
Given a holomorphic differential on a smooth complex algebraic curve, we associate to it a Gorenstein curve singularity with $\mathbb G_m$-action via a test configuration. This construction decomposes the strata of holomorphic differentials…
We prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective…
In $D=2+1$ dimensions, elementary particles of a given helicity can be described by local Lagrangians (parity singlets). By means of a "soldering" procedure two opposite helicities can be joined together and give rise to massive spin-$s$…
We construct a modular desingularisation of $\overline{\mathcal{M}}_{2,n}(\mathbb{P}^r,d)^{\text{main}}$. The geometry of Gorenstein singularities of genus two leads us to consider maps from prestable admissible covers: with this enhanced…
Relations between Gorenstein derived categories, Gorenstein defect categories and Gorenstein stable categories are established. Using these, the Gorensteinness of an algebra $A$ and invariants with respect to recollements of the bounded…
In this paper, we study nearly Gorensteinness of Ehrhart rings arising from lattice polytopes. We give necessary conditions and sufficient conditions on lattice polytopes for their Ehrhart rings to be nearly Gorenstein. Using this, we give…
Unlike the Gorenstein projective and injective dimensions, the majority of results on the Gorenstein flat dimension have been established only over Noetherian (or coherent) rings. Naturally, one would like to generalize these results to any…
We give a generalization of the duality of a zero-dimensional complete intersection to the case of one-dimensional almost complete intersections, which results in a {\em Gorenstein module} $M=I/J$. In the real case the resulting pairing has…
Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. This paper proves that M is a dualizing complex for A if and only if the trivial extension A \ltimes M is a Gorenstein Differential Graded Algebra.…
In this paper, binary extremal singly even self-dual codes of length 40 and extremal odd unimodular lattices in dimension 40 are studied. We give a classification of extremal singly even self-dual codes of length 40. We also give a…