We show that the cobordism group of fold maps of even non-positive codimension q into a manifold N is a sum of q/2 cobordism groups of framed immersions into N and a group related to diffeomorphism groups of manifolds of dimension q + 1. In the case of maps of odd non-positive codimension q, we show that the cobordism groups of fold maps split off (q − 1)/2 cobordism groups of framed immersions.

We examine the recently found point of intersection between the Z2 and Z4 orbifold subvarieties in the K3 moduli space more closely. First we give an explicit identification of the coordinates of the respective Z2 and Z4 orbifold theories at this point. Secondly we construct the explicit identification of conformal field theories at this point and show the orthogonality of the two subvarieties.

The conjecture on the (degree − codimension+ 1)regularity of projective varieties is proved for smooth linearly normal polarized varieties (X, L) with L very ample, for low values of ∆(X, L) = degree− codimension− 1. Results concerning the projective normality of some classes of special varieties including scrolls over curves of genus 2 and quadric fibrations over elliptic curves, are proved.

We study the algebraization problem for principal bundles with reductive structure groups on a non-proper formal scheme. When the formal scheme can be compactified by adding a closed subset of codimension at least 3, we show that any such bundle admits an algebraization. For codimension 2 we provide a necessary and sufficient condition.

Let F be a foliation of codimension 2 on a compact manifold with at least one non-compact leaf. We show that then F must contain uncountably many non-compact leaves. We prove the same statement for oriented p-dimensional foliations of arbitrary codimension if there exists a closed p form which evaluates positively on every compact leaf. For foliations of codimension 1 on compact manifolds it is...

We study the matching conditions of intersecting brane worlds in Lovelock gravity in arbitrary dimension. We show that intersecting various codimension 1 and/or codimension 2 branes one can find solutions that represent energymomentum densities localized in the intersection, providing thus the first examples of infinitesimally thin higher codimension braneworlds that are free of singularities a...

The positive characteristic function-field Mordell-Lang conjecture for finite rank subgroups is resolved for curves as well as for subvarieties of semiabelian varieties defined over finite fields. In the latter case, the structure of the division points on such subvarieties is determined.

We study Stanley decompositions and show that Stanley’s conjecture on Stanley decompositions implies his conjecture on partitionable Cohen-Macaulay simplicial complexes. We also prove these conjectures for all Cohen-Macaulay monomial ideals of codimension 2 and all Gorenstein monomial ideals of codimension 3.

In this paper we deal with reversible vector fields on a 2-dimensional manifold having a codimension one submanifold as its symmetry axis. We classify generically the one parameter families of such vector fields. As a matter of fact, aspects of structural stability and codimension one bifurcation are analysed.