Notes on Compactification. I

Stable Compactification I

This paper represents a continuation of our programme [16, 13] of extending various concepts of general topology from the setting of Hausdorff (or, at most, 7̂ ) spaces, in which they are usually embedded, to the larger classes of spaces we need to consider in the theory of computation. The topic of compactification poses an obvious challenge to this programme, since only a Tychonoff space can h...

Parabolic Bundles on Algebraic Surfaces I- the Donaldson–uhlenbeck Compactification

The aim of this paper is to construct the parabolic version of the Donaldson–Uhlenbeck compactification for the moduli space of parabolic stable bundles on an algenraic surface with parabolic structures along a divisor with normal crossing singularities. We prove the non–emptiness of the moduli space of parabolic stable bundles of rank 2 and also prove the existence of components with smooth po...

Notes on Sandflies. Part I

I. Notes on Structured Programming

These notes have the status of "Letters written to myself": I wrote them down because, without doing so, I found myself repeating the same arguments over and over again. When reading what I had written, I was not always too satisfied. For one thing, I felt that they suffered from a marked verbosity. Yet I do not try to condense them (now), firstly because that would introduce another delay and ...

Intersecting Brane World From Type I Compactification

We elaborate that general intersecting brane models on orbifolds are obtained from type I string compactifications and their T -duals. Symmetry breaking and restoration occur via recombination and parallel separation of branes, preserving supersymmetry. The Ramond– Ramond tadpole cancelation and the toron quantization constrain the spectrum as a branching of the adjoints of SO(32), up to orbifo...