We explicitly describe the KSBA/Hacking compactification of a moduli space of log surfaces
of Picard rank 2. The space parametrizes log pairs $(S, D) $ where $ S $ is a degeneration …

This paper classifies proper birational morphisms of smooth threefolds collapsing three
smooth surfaces meeting normally to a point. In addition to three blow-ups and Hironaka's …

The factorization problem, which has been an open question for some forty years, asks
whether any birational correspondence fbetween algebraic spaces or varieties can be" …

THEOREM 1. Let T be an algebraic torus. Suppose that X is a normal variety isomorphic in
codimension one to a torus embedding-ie, X less a subset of codimen-sion at least two is …

The main result is the proof of the fact that one can perform a finite number of monoidal
transformations with nonsingular centers in such a way that any two nonsingular birationally …

Using combinatorial methods, we classify all birational morphisms blowing m≦ 5 divisors
down to a point. Those which do not factor through the blowing up of a point are treated in …

Zariski proved around 1944 that every birational morphism between smooth surfaces over a
field k is a composition of blowing-ups at closed points. Later, around 1966 Shafarevich …

The paper introduces formally the concept of local factorizability used in earlier factorizability
work, identifies the basic form of obstructions to local factorizability of birational morphisms …

В более слабой форме речь идет о разложимости/в произведение чередующихся
композиций а-процессов и обратных к ним. В случае поверхностей положительное …

We consider a proper birational morphism f: XY of regular schemes in this paper. The
fundamental locus S (f) of f, ie, the set where f'is not well-defined, may be singular. An …