Related papers: Andr\'{e}-Quillen homology and complete intersecti…
We study a natural model of random 2-dimensional cubical complex which is a subcomplex of an n-dimensional cube, and where every possible square $2$-face is included independently with probability p. Our main result is to exhibit a sharp…
The recent link discovered between generalized Legendre transforms and non-dually flat statistical manifolds suggests a fundamental reason behind the ubiquity of R\'{e}nyi's divergence and entropy in a wide range of physical phenomena.…
The set of subspaces with a given dimension in an attenuated space has a structure of a symmetric association scheme, which is a generalization of both Grassmann schemes and bilinear forms schemes. In [K. Wang, J. Guo, F. Li, Association…
The quantum cohomology algebra of a projective manifold X is the cohomology H(X,Q) endowed with a different algebra structure, which takes into account the geometry of rational curves in X. We show that this algebra takes a remarkably…
We introduce a new homology theory of quandles, called simplicial quandle homology, which is quite different from quandle homology developed by Carter et al. We construct a homomorphism from a quandle homology group to a simplicial quandle…
This is a survey on the relation between homological properties of the Frobenius endomorphism and finiteness of various homological dimensions of the ring or of modules over it, such as global dimension and projective dimension. We begin…
Let $M,N$ be finitely generated modules over a local complete intersection $R$. Assume that for each $i>0$, $\mathrm{Tor}^R_i(M,N)=0$. We prove that the cohomological support of $M\otimes_R N$ (in the sense of Avramov-Buchweitz) is equal to…
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
Let $R$ be semiperfect commutative Noetherian ring and $C$ be a semidualizing $R$--module. The connection of the Serre condition $(S_n)$ on a horizontally linked $R$-module of finite $\gc$-dimension with the vanishing of certain cohomology…
In his study of the group of homology cylinders, J. Levine made the conjecture that a certain homomorphism eta': T -> D' is an isomorphism. Here T is an abelian group on labeled oriented trees, and D' is the kernel of a bracketing map on a…
Here we explore a variety of properties of intrinsic flat convergence. We introduce the sliced filling volume and interval sliced filling volume and explore the relationship between these notions, the tetrahedral property and the…
In this paper we describe all possible reduced complete intersection sets of points on Veronese surfaces. We formulate a conjecture for the general case of complete intersection subvarieties of any dimension and we prove it in the case of…
The aim of this work is to clarify the relationship between homology theory of commutative monoids constructed 'a la Quillen and technology of Gamma-modules.
The simplest i.e. the Abelian i.e. the commutative i.e. the integrable i.e. the flat and torsion-free i.e. the symmetric teleparallel affine connection has been considered in many recent works in the literature. Such an affine connection is…
A short review of the history and a 'slide-show' of QCD tests in $e^+e^-$ annihilation is given. The world summary of measurements of $\alpha_s$ is updated.
For a smooth quasi-projective surface S over complex numbers we consider the Borel-Moore homology of the stack of coherent sheaves on S with compact support and make this space into an associative algebra by a version of the Hall…
This paper improves several previously known results. First, the results describing the R-skewsymmetric algebra and the quadratic dual of the R-symmetric algebra as Frobenius algebras are shown to be true with any restriction on the…
We study QCD on AdS space with scalars or fermions in the fundamental representation, extending earlier results on pure Yang-Mills theory. In the latter, the Dirichlet boundary condition is conjectured to disappear via merger and…
We prove that the homology groups of any connected reductive group over a field with coefficients in the Steinberg representation vanish in a range. The generalizes work of Ash-Putman-Sam on the classical split groups. We state a…
We study the relationship between positivity of line bundles restricted to complete intersection subvarieties and the vanishing of higher cohomology groups. Based on this connection we prove generalizations of the vanishing theorems of…