相关论文: A Note On Gorenstein Injective Dimension
In this manuscript, we provide a concise review of the concept of metric dimension for both deterministic as well as random graphs. Algorithms to approximate this quantity, as well as potential applications, are also reviewed. This work has…
In this paper, we study Gorenstein injective, projective, and flat modules over a Noetherian ring $R$. For an $R$-module $M$, we denote by ${\rm Gpd}_RM$ and ${\rm Gfd}_R M$ the Gorenstein projective and flat dimensions of $M$,…
This paper forms part of a larger work where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of "global conformal invariants"; these are defined to be conformally invariant integrals of geometric scalars. The…
Answering a question of M. Reid, we define and prove the Gorensteiness of the type II unprojection.
The global dimension of a triangulated category is defined to be the infimum value of the global dimensions of stability conditions on the triangulated category. In this paper, we study the global dimension of the derived category of an…
We prove addition and subspace theorems for asymptotic large inductive dimension. We investigate a transfinite extension of this dimension and show that it is trivial.
Using the method of degenerating a Grassmannian into a toric variety, we calculate recursive formulas for the dimensions of the eigenspaces of the action of an n-dimensional torus on a Grassmannian of planes in an n-dimensional space. In…
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…
For a dualizing module $D$ over a commutative Noetherian ring $R$ with identity, it is known that its Auslander class $\mathscr{A}_D\left(R\right)$ (respectively, Bass class $\mathscr{B}_D\left(R\right)$) is characterized as those…
Warped embeddings from a lower dimensional Einstein manifold into a higher dimensional one are analyzed. Explicit solutions for the embedding metrics are obtained for all cases of codimension 1 embeddings and some of the codimension n>1…
I propose a few increasingly stronger "superadditivity" conjectures regarding the behavior of Kodaira dimension under morphisms of smooth quasi-projective complex varieties.
Firstly, we introduce a new notion called induced upper metric mean dimension with potential, which naturally generalizes the definition of upper metric mean dimension with potential given by Tsukamoto to more general cases, then we…
We prove Rapoport's dimension conjecture for affine Deligne-Lusztig varieties for GL_h and superbasic b. From this case the general dimension formula for affine Deligne-Lusztig varieties for special maximal compact subgroups of split groups…
We relate the notion of dimension expanders to quiver representations and their general subrepresentations, and use this relation to establish sharp existence results.
In this paper we study the finiteness of global Gorenstein AC-homological dimensions for rings, and answer the questions posed by Becerril, Mendoza, P\'{e}rez and Santiago. As an application, we show that any left (or right) coherent and…
We begin by explaining how to compute Fourier expansions at all cusps of any modular form of integral or half-integral weight thanks to a theorem of Borisov-Gunnells and explicit expansions of Eisenstein series at all cusps. Using this, we…
We give a formula to compute the dimension of the generic component of the moduli space of an irreducible germ of curve in the complex plane.
We present a new type of integral that is supposed to extend the usability of the Lebesgue integral in certain types of investigations. It is based on the Hausdorff dimension and measure. We examine the basic properties of the integral and…
A formula which expresses logarithmic energy of Borel measures on R^n in terms of the Fourier transforms of the measures is established and some applications are given. In addition, using similar techniques a (known) formula for Riesz…
The Galilean invariance in three dimensional space-time is considered. It appears that the Galilei group in 2+1 dimensions posses a three-parameter family of projective representations. Their physical interpretation is discussed in some…