A Further Extension of the KKMS Theorem

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

An extension of the Wedderburn-Artin Theorem

‎In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.

An extension theorem for finite positive measures on surfaces of finite‎ ‎dimensional unit balls in Hilbert spaces

A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...

Weak Semistable Reduction in Characteristic 0 Preliminary Version

0.1. The problem. Roughly speaking, the semistable reduction problem we address here asks for the following: Let X → B be a surjective morphism of complex projective varieties with geometrically integral generic fiber. Find a generically finite proper surjective morphism (that is, an alteration) B1 → B, and a proper birational morphism (that is, a modification) Y → X ×B B1, such that the morphi...

Semistable Reduction in Characteristic Zero for Families of Surfaces and Threefolds

We consider the problem of extending the semistable reduction theorem of [KKMS] from the case of one-parameter families of varieties to families over a base of arbitrary dimension. Following [KKMS], semistable reduction of such families can be reduced to a problem in the combinatorics of polyhedral complexes [AK]. In this paper we solve it in the case when the relative dimension of the morphism...