Related papers: Compactification projective de Spec Z (d'apres Dur…

This is part I of a three-part series of papers, whose aim is to develop a theory of discrete localities. These generalize the p-local compact groups of Broto, Levi, and Oliver.

In this paper we first note a result of birational automorphisms with bounded degree of projective varieties related with the Zariski dense orbit conjecture (ZDO) and the Zariski density of periodic points. Next, we give a reduced result of…

This is my dissertation about digraphs ordered by pp-constructability. We study in particular smooth digraphs, i.e., digraphs without sources or sinks, tournaments and semicomplete digraphs, orientations of paths and cycles, digraphs with…

An overview of the recent developments in plurifine potential theory.

This monograph is on convex real projective structures on strongly tame n-orbifolds with some appropriate conditions on ends.

This is a survey of the theory of complex projective (CP^1) structures on compact surfaces. After some preliminary discussion and definitions, we concentrate on three main topics: (1) Using the Schwarzian derivative to parameterize the…

In this paper we give a generalization of injective and projective complexes.

This paper has been subsumed by math.AG/0502240

This is a report on the recent work "Mirror symmetry for exceptional unimodular singularities" joint with Changzheng Li, Si Li and Yefeng Shen.

Compactness is one of the most versatile tools in the analysis of nonlinear PDEs and systems. Usually, compactness is established by means of some embedding theorem between functional spaces. Such theorems, in turn, rely on appropriate…

In this paper, we characterize smooth projective surfaces on which every integral pseudoeffective divisor has an integral Zariski decomposition.

This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).

We give an introduction to the compactification of the moduli space of surfaces of general type introduced by Koll\'ar and Shepherd-Barron and generalized to the case of surfaces with a divisor by Alexeev. The construction is an application…

We present a version of the Penrose transform which relates compactly supported cohomology on a complex or CR manifold Z to kernels and cokernels of differential operators on a parameter space X of compact complex submanifolds of Z.

Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…

Semistable reduction theorem for projective morphisms in the category of complex analytic spaces is established.

We discuss possible discretizations of complex analysis and some of their applications to probability and mathematical physics, following our recent work with Dmitry Chelkak, Hugo Duminil-Copin and Cl\'ement Hongler.

Let V be a complex vector space. We propose a compactification PM(V) of the projective linear group PGL(V), which can act on the projective space P(V). After proving some properties of PM(V), we consider its relation to Neretin's…

This article will appear in the Encyclopedia of Mathematical Physics (Elsevier, 2006) and follows its referencing guidelines.

We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.