1. All operators will be supposed bounded, linear (everywhere defined) over a Hilbert space. By the commutator, C, of two operators A and B will be meant the operator (1) C = AB BA. A conjecture of Kaplansky, cited in [4], that if A commutes with C, so that (2) AC = CA, then (3) sp(C) = 0 only (sp = spectrum), was recently proved by Kleinecke [6] and Shirokov [9]. Earlier proofs of (3) under th...

Let X be a normal arithmetically Gorenstein scheme in P. We give a criterion for all codimension two ACM subschemes of X to be in the same Gorenstein biliaison class on X, in terms of the category of ACM sheaves on X. These are sheaves that correspond to the graded maximal Cohen–Macaulay modules on the homogeneous coordinate ring of X. Using known results on MCM modules, we are able to determin...

We describe the structure, including composition factors and submodule lattices, of cross-characteristic permutation modules for the natural actions of the orthogonal groups O± m(3) with m ≥ 6 on nonsingular points of their standard modules. These actions together with those studied in [2] are all examples of primitive rank 3 actions of finite classical groups on nonsingular points.

We introduce a class extending the notion of Chern-Mather class to possibly nonreduced schemes, and use it to express the di erence between SchwartzMacPherson's Chern class and the class of the virtual tangent bundle of a singular hypersurface of a nonsingular variety. Applications include constraints on the possible singularities of a hypersurface and on contacts of nonsingular hypersurfaces, ...

A toroidalization of a dominant morphism $varphi: Xto Y$ of algebraic varieties over a field of characteristic zero is a toroidal lifting of $varphi$ obtained by performing sequences of blow ups of nonsingular subvarieties above $X$ and $Y$. We give a proof of toroidalization of locally toroidal morphisms of 3-folds.

the concept of fuzzy soft γ-ring is introduced; and some properties of fuzzy soft γ-rings are given. then the definitions of fuzzy soft γ-ideals are proposed and some of their theories are considered.

In this paper, we investigate whether the 124 nonsingular toric Fano 4-folds admit totally nondegenerate embeddings from abelian surfaces or not. As a result, we determine the possibilities for such embeddings except for the remaining 21 nonsingular toric Fano 4-folds.

In this paper, we first review the PU and Uzawa-SAOR relaxation methods with singular or nonsingular preconditioning matrices for solving singular saddle point problems, and then we provide numerical experiments to compare performance results of the relaxation iterative methods using nonsingular preconditioners with those using singular preconditioners. Mathematics Subject Classification: 65F10...

Suppose that X is a nonsingular variety and D is a nonsingular proper subvariety. Configuration spaces of distinct and non-distinct n points in X away from D were constructed by the author and B. Kim in [4] by using the method of wonderful compactification. In this paper, we give an explicit presentation of Chow motives and Chow rings of these configuration spaces.

In this paper a closing lemma for C1 nonsingular endomorphisms equivariant under free actions of finite-groups is proved. Hence a recurrent trajectory, as well as all of its symmetric conjugates, of a C1 nonsingular endomorphism equivariant under a free action of a finite group can be closed up simultaneously by an arbitrarily small C1 equivariant perturbation.