In this paper – a sequel to [14] – we obtain existence and approximation results for closed complex subvarieties that are normalized by strongly pseudoconvex Stein domains. Our sufficient condition for the existence of such subvarieties in a complex manifold X is expressed in terms of the Morse indices and the number of positive Levi eigenvalues of an exhaustion function on X. Examples show tha...

In this article, we provide a complete list of simple isolated CohenMacaulay codimension 2 singularities together with a list of adjacencies which is complete in the case of fat point and space curve singularities.

For a given sequence of integers (ni) ∞ i=1 we consider all the central simple algebras A (over all fields) satisfying the condition ind A = ni and find among them an algebra having the biggest torsion in the second Chow group CH of the corresponding Severi-Brauer variety (“biggest” means that it can be mapped epimorphically onto each other). We describe this biggest torsion in a way in general...

We study conditions under which a finite simplicial complex K can be mapped to R without higher-multiplicity intersections. An almost r-embedding is a map f : K → R such that the images of any r pairwise disjoint simplices of K do not have a common point. We show that if r is not a prime power and d ≥ 2r + 1, then there is a counterexample to the topological Tverberg conjecture, i.e., there is ...

We describe classes of toric varieties of codimension 2 which are either minimally defined by codim V +1 binomial equations over any algebraically closed field, or set-theoretic complete intersections in exactly one positive characteristic .

We single out some problems of Schubert calculus of subspaces of codimension 2 that have the property that all their solutions are real whenever the data are real. Our arguments explore the connection between subspaces of codimension 2 and rational functions of one variable.

We find a sufficient condition that H is not level based on a reduction number. In particular, we prove that a graded Artinian algebra of codimension 3 with Hilbert function H = (h0, h1, . . . , hd−1 > hd = hd+1) cannot be level if hd ≤ 2d + 3, and that there exists a level Osequence of codimension 3 of type H for hd ≥ 2d+k for k ≥ 4. Furthermore, we show that H is not level if β1,d+2(I ) = β2,...

As usual, Z,Q,C denote the ring of integers, the field of rational numbers and the field of complex numbers respectively. Let us fix a primitive cube root of unity ζ3 = −1+ √ −3 2 ∈ C. Let Q(ζ3) = Q( √ −3) be the third cyclotomic field and Z[ζ3] = Z +Z · ζ3 its ring of integers. We write λ for the (principal) maximal ideal (1− ζ3) · Z[ζ3] of Z[ζ3]. It is known [11, Th. 5 on p. 176] (see also [5...