Imbedding of an abstract variety in a complete variety

The Quotient of a Complete Symmetric Variety

We study the quotient of a completion of a symmetric variety G/H under the action of H . We prove that this is isomorphic to the closure of the image of an isotropic torus under the action of the restricted Weyl group. In the case the completion is smooth and toroidal we describe the set of semistable points. 2000 Math. Subj. Class. 14L30, 14L24, 14M17.

On the Quotient Variety of an Abelian Variety.

An interesting variety

This issue of Neurology ® : Neuroimmunology and Neu-roinflammation (N2) includes a wide variety of exciting articles. As usual, I had difficulty selecting the articles to highlight in this Editor's Corner, which is aimed to reflect the range of topics rather than imply a higher quality of the selected manuscripts. One of the treatments frequently used in neuro-myelitis optica (NMO) is rituximab...

The Ring of Sections of a Complete Symmetric Variety

We study the ring of sections A(X) of a complete symmetric variety X, that is of the wonderful completion of G/H where G is an adjoint semi-simple group and H is the fixed subgroup for an involutorial automorphism of G. We find generators for Pic(X), we generalize the PRV conjecture to complete symmetric varieties and construct a standard monomial theory for A(X) that is compatible with G orbit...

An uncommon variety of brachydactyly

Introduction The word brachydactyly is used to describe the hands and feet with shortened digits (brachy, meaning “short,” and daktylos, meaning “digit”) [1]. The digits themselves may be shorter than normal or they may appear small because of shortening of metacarpal and metatarsal bones in the hands or feet [1]. Most of the patients with brachydactyly do not require any specific treatment. Wh...