Related papers: Maximal Cohen-Macaulay modules over non-isolated s…
Let A be a commutative k-algebra, where k is an algebraically closed field of characteristic 0, and let M be an A-module. We consider the following question: Under what conditions on A and M is it possible to find a connection on M? We…
Given a hyper loop algebra over a non-algebraically closed field, we address multiplicity problems in the underlying abelian tensor category of finite-dimensional representations. Namely, we give formulas for the l-characters of the simple…
In this paper, we introduce initially Cohen-Macaulay modules over a commutative Noetherian local ring $R$, a new class of $R$-modules that generalizes both Cohen-Macaulay and sequentially Cohen-Macaulay modules. A finitely generated…
Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. We exhibit slices of the representation theory of $\Lambda$ that are always classifiable in stringent geometric terms. Namely, we prove that, for any…
In two parts, we present a bigness criterion for the cotangent bundle of resolutions of orbifold surfaces of general type. As a corollary, we obtain the \textit{canonical model singularities} (CMS) criterion that can be applied to determine…
Recently, G. Floystad studied "higher Cohen-Macaulay property" of certain finite regular cell complexes. In this paper, we partially extend his results to squarefree modules, toric face rings, and simplicial posets. For example, we show…
Mather and Yau showed that an isolated complex hypersurface singularity is completely determined by its moduli algebra. It is shown, for the simple elliptic singularities, how to construct continuous invariants from the moduli algebras and,…
We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…
The work is a detailed study of rational singularities of multiplicity 3 (RTP-singularities, for short). We give a list of nonisolated hypersurface singularities of which normalisations are the RTP-singularities, and construct their minimal…
We extend the notion of representation of a matroid to algebraic structures that we call skew partial fields. Our definition of such representations extends Tutte's definition, using chain groups. We show how such representations behave…
Isolated Cohen-Macaulay codimension 2 singularities share many common features with isolated complete intersection singularities, but they also exhibit some striking new behaviour. One such instance was recently observed by Damon and Pike…
Let $S$ be a punctured surface of finite type and negative Euler characteristic. We determine all possible representations $\rho:\pi_1(S) \to \text{PSL}_2(\mathbb{C})$ that arise as the monodromy of the Schwarzian equation on $S$ with…
This paper studies the structure of special preenvelopes and envelopes with respect to maximal Cohen-Macaulay modules. We investigate the structure of them in terms of their kernels and cokernels. Moreover, using this result, we also study…
We prove some results on the non-existence of rank one maximal Cohen-Macaulay modules over certain Segre product rings. As an application we show that over these Segre product rings there do not exist maximal Cohen-Macaulay modules with…
Consider a linear realization of a matroid over a field. One associates with it a configuration polynomial and a symmetric bilinear form with linear homogeneous coefficients. The corresponding configuration hypersurface and its non-smooth…
We study a class of overdetermined algebraic systems of equations. We prove that the number of distinct solutions equals to the maximal possible if and only if certain matrices are commuting and semisimple. This gives a characterization of…
We first generalize classical Auslander-Reiten duality for isolated singularities to cover singularities with a one-dimensional singular locus. We then define the notion of CT modules for non-isolated singularities and we show that these…
In this paper we show that the (co)chain complex associated with a decomposition of the computational domain, commonly called a mesh in computational science and engineering, can be represented by a block-bidiagonal matrix that we call the…
It is shown that if $X$ is an Inoue surface of type $S_M$ then the irreducible components of the Douady space of $X^n$ are compact, for all $n>0$. This gives an example of an essentially saturated compact complex manifold (in the sense of…
Over a Cohen-Macaulay (CM) local ring, we characterize those modules that can be obtained as a direct limit of finitely generated maximal CM modules. We point out two consequences of this characterization: (1) Every balanced big CM module,…