In this article, we prove that any Q-factorial weak Fano 3-fold with only terminal singularities has a smoothing. 0. Introduction Definition 0.1. Let X be a normal Gorenstein projective variety of dimension 3 over C which has only terminal singularities. (1) If −KX is ample, we call X a Fano 3-fold. (2) If −KX is nef and big, we call X a weak Fano 3-fold. Definition 0.2. Let X be a normal Goren...

We generalize the theory developed by K. Takeuchi in [T1] and restrict the birational type of a Q-factorial Q-Fano 3-fold X with the following properties: (1) the Picard number of X is 1; (2) the Gorenstein index of X is 2; (3) the Fano index of X is 1 2 ; (4) h(−KX) ≥ 4; (5) there exists an index 2 point P such that (X, P ) ≃ ({xy + f(z, u) = 0}/Z2(1, 1, 1, 0), o) with ordf(Z, U) = 1. This giv...

Abstract The purpose of this paper is to lay the foundations for study problem when in Banach spaces. We provide a number examples couples $X$?> , $Y$?> such that $\operatorname{Ext}^n(X,Y)$?> (or not) $0$?> . show $\operatorname{Ext}^n(\mathcal K, \mathcal K)\neq 0$?> all $n\in \mathbb{N}$?> $\mathcal K$?> Kadec space. In particular, both projective and...

If V is an equidimensional codimension c subscheme of an n-dimensional projective space, and V is linked to V ′ by a complete intersection X, then we say that V is minimally linked to V ′ if X is a codimension c complete intersection of smallest degree containing V . Gaeta showed that if V is any arithmetically Cohen-Macaulay (ACM) subscheme of codimension two then there is a finite sequence of...

‎Let $mathcal{F}$ be an field of zero characteristic and $N_{infty‎}(‎mathcal{F})$ be the algebra of infinite strictly upper triangular‎ ‎matrices with entries in $mathcal{F}$‎, ‎and $f:N_{infty}(mathcal{F}‎)rightarrow N_{infty}(mathcal{F})$ be a non-additive Lie centralizer of $‎N_{infty }(mathcal{F})$; that is‎, ‎a map satisfying that $f([X,Y])=[f(X),Y]$‎ ‎for all $X,Yin N_{infty}(mathcal{F})...

In this paper, we investigate the relative dominant dimension with respect to an injective module and characterize algebras finite dimension. As application, introduce almost n-precluster tilting establish a correspondence between modules n-minimal Auslander-Gorenstein algebras. Moreover, give description of Gorenstein projective over in terms corresponding modules.

The classical global and weak dimensions of rings play an important role in the theory of rings and have a great impact on homological and commutative algebra. In this paper, we define and study the Gorenstein homological dimensions of commutative rings (Gorenstein projective, injective, and flat dimensions of rings) which introduce a new theory similar to the one of the classical homological d...

Let X denote an integral, projective Gorenstein curve over an algebraically closed field k. In the case when k is of characteristic zero, C. Widland and the second author ([22], [21], [13]) have defined Weierstrass points of a line bundle on X. In the first section, we extend this by defining Weierstrass points of linear systems in arbitrary characteristic. This definition may be viewed as a ge...

in this work‎, ‎an iterative method based on a matrix form of lsqr algorithm is constructed for solving the linear operator equation $mathcal{a}(x)=b$‎ ‎and the minimum frobenius norm residual problem $||mathcal{a}(x)-b||_f$‎ ‎where $xin mathcal{s}:={xin textsf{r}^{ntimes n}~|~x=mathcal{g}(x)}$‎, ‎$mathcal{f}$ is the linear operator from $textsf{r}^{ntimes n}$ onto $textsf{r}^{rtimes s}$‎, ‎$ma...

Let M be a monoid and \(G:\mathbf {Mon} \rightarrow \mathbf {Grp}\) the group completion functor from monoids to groups. Given collection \(\mathcal {X}\) of submonoids for each \(N\in \mathcal {Y}_N\) subgroups G(N), we construct model structure on category M-spaces M-equivariant maps, called \((\mathcal {X},\mathcal {Y})\)-model structure, in which weak equivalences fibrations are induced sta...