Some remarks on varieties with degenerate Gauss image

We consider projective varieties with degenerate Gauss image whose focal hypersurfaces are non-reduced schemes. Examples of this situation are provided by the secant varieties of Severi and Scorza varieties. The Severi varieties are moreover characterized by a uniqueness property.Comment: 9 pages, to be published in Pacific Journal of Mathematic

Proof of the Knop conjecture

In this paper we prove the Knop conjecture asserting that two smooth affine spherical varieties with the same weight monoids are equivariantly isomorphic. We also state and prove a uniqueness property for not necessarily smooth affine spherical varietiesComment: 31 pages, v2,v3 typos fixed, minor mistakes are corrected, references added v4 20 pages, crucial changes made. The proof now uses results of AG/0703543. A new result concerning a uniqueness property of not necessarily smooth affine spherical varieties is added, v6 final version, to appear in Annales de l Institut Fourie

Customization: Ideal Varieties, Product Uniqueness and Price Competition

We study customization in the Hotelling model with two firms. In addition to providing ideal varieties, the perceived uniqueness of a customized product contributes independently to consumer utility. We show that only when consumer preferences for uniqueness are high customization occurs in equilibrium.customization, product differentiation, product uniqueness, price competition

Customization: Ideal Varieties, Product Uniqueness and Price Competition

We study customization in the Hotelling model with two firms. In addition to providing ideal varieties, the perceived uniqueness of a customized product contributes independently to consumer utility. We show that only when consumer preferences for uniqueness are high customization occurs in equilibrium

Wonderful varieties of type D

Let G be a complex connected semisimple group, whose simple components have type A or D. We prove that wonderful G-varieties are classified by means of combinatorial objects called spherical systems. This is a generalization of a known result of Luna for groups of type A; thanks to another result of Luna, this implies also the classification of all spherical G-varieties for the groups G we are considering. For these G we also prove the smoothness of the embedding of Demazure.Comment: 60 pages, AMSLaTeX, 11 eps file