Let X be a nonsingular algebraic variety. Suppose Z ⊆ X is a closed subscheme of X, with ideal sheaf IZ . When Z has codimension one in X, everything is as nice as it could be: IZ is a locally free sheaf, in fact a line bundle, and Z can locally be defined by a single equation. But starting in codimension two, all these pleasant things are usually false. To begin with, not every closed subschem...

In this paper we show how the restriction of the complex algebraic cycles to real part of a complex algebraic set îs related to the real algebraic cycles of the real part As a corollary we give examples of smooth submanifolds of a Euchdean space which can not be isotoped to real parts of complex nonsingular subvaneties in the corresponding projective space Algebraic numbers are dense in R. The ...

The classical Poisson functor associates to every infinite measure preserving dynamical system (X, μ, T) a probability (X*, μ*, T*) called the suspension of T. In this paper we generalize construction: subgroup Aut2(X, μ) μ-nonsingular transformations T X is specified as largest for which T* μ*-nonsingular. topological structure studied. We show that generic element in ergodic and Krieger type ...

It is the purpose of this note to point out that there may also exist bounded regions which exclude the latent roots of A. Let B: [&,-,•] be an nXn matrix with complex elements. Let (/i(l), • • ■ , n(n)) be a permutation of (1, • • • , n), and let B'\ [b'tj] be the matrix [b'v] = [&*.(,•)]. Thus£' is obtained from B by a permutation of its columns, and therefore B is nonsingular when B' is nons...

A new version of the inflationary universe scenario is suggested which provides a possible solution of the cosmological singularity

We examine the possibility that time dependence might remove the singular nature of global string spacetimes. We first show that this time dependence takes a specific form – a de-Sitter like expansion along the length of the string and give an argument for the existence of such a solution, estimating the rate of expansion. We compare our solution to the singular Cohen-Kaplan spacetime. PACS num...

Let X be an arbitrary nonsingular projective 3-fold whose canonical bundle is not numerically effective. Then we have: (i) X contains an exceptional divisor of several types, which we classify explicitly, (ii) X has a morphism to a projective nonsingular surface whose fibers are conics, (iii) X has a morphism to a projective nonsingular curve whose general fibers are Del Pezzo surfaces, or (iv)...

For nonsingular n× n (n ≥ 6) pentadiagonal matrices P having nonzero entries on its second subdiagonal, we propose a procedure for computing both the determinant detP in O(n) times, and accurate information for obtaining the inverse P−1 in O(n) times. In the general nonsingular case, n ≥ 5, a suitable decomposition of P, as a product of two nonsingular upper Hessenberg matrices, allows us anoth...

We show that a nef and big line bundle whose adjoint bundle has non-zero global sections on a nonsingular toric weak Fano 3-fold is normally generated. As a consequence, we see that any ample line bundle on a nonsingular toric waek Fano 3-fold is normally generated. As an application, we see that an ample line bundle on a Calabi-Yau hypersurface in a nonsingular toric Fano 4-fold is normally ge...

The fast matrix multiplication algorithm by Strassen is used to obtain the triangular factorization of a permutation of any nonsingular matrix of ordern in <Cxnlos'7 operations, and, hence, the inverse of any nonsingular matrix in <Cürtlog'7 operations.