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Classification of obstructions for separation of semialgebraic sets in dimension 3.

F. Acquistapace, F. Broglia, C. Andradas (1997)

Revista Matemática de la Universidad Complutense de Madrid

Applying general results on separation of semialgebraic sets and spaces of orderings, we produce a catalogue of all possible geometric obstructions for separation of 3-dimensional semialgebraic sets and give some hints on how separation can be made decidable.

Classification of spherical varieties

Paolo Bravi (2010)

Les cours du CIRM

We give a short introduction to the problem of classification of spherical varieties, by presenting the Luna conjecture about the classification of wonderful varieties and illustrating some of the related currently known results.

Classification of strict wonderful varieties

Paolo Bravi, Stéphanie Cupit-Foutou (2010)

Annales de l’institut Fourier

In the setting of strict wonderful varieties we prove Luna’s conjecture, saying that wonderful varieties are classified by combinatorial objects, the so-called spherical systems. In particular, we prove that primitive strict wonderful varieties are mostly obtained from symmetric spaces, spherical nilpotent orbits and model spaces. To make the paper as self-contained as possible, we also gather some known results on these families and more generally on wonderful varieties.

Clifford’s Theorem for real algebraic curves

Jean-Philippe Monnier (2010)

Annales de l’institut Fourier

We establish, for smooth projective real curves, an analogue of the classical Clifford inequality known for complex curves. We also study the cases when equality holds.

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