Generalized Fréchet varieties

On real generalized Jacobian varieties

In this note, we study effective Cartier divisors with totally real or totally complex supports on a projective curve over R. We give some numerical conditions for an invertible sheaf to be isomorphic or not to such a divisor. We show that these conditions are strongly related to the singularities of the curve and to topological properties of the real part of the Jacobian variety.

Singularities of Generalized Richardson Varieties

Richardson varieties play an important role in intersection theory and in the geometric interpretation of the Littlewood-Richardson Rule for flag varieties. We discuss three natural generalizations of Richardson varieties which we call projection varieties, intersection varieties, and rank varieties. In many ways, these varieties are more fundamental than Richardson varieties and are more easil...

On Sifted Colimits and Generalized Varieties

Filtered colimits, i.e., colimits over schemes D such that D-colimits in Set commute with finite limits, have a natural generalization to sifted colimits: these are colimits over schemes D such that D-colimits in Set commute with finite products. An important example: reflexive coequalizers are sifted colimits. Generalized varieties are defined as free completions of small categories under sift...

Generalized MSTB Models : Structure and kink varieties

In this paper we describe the structure of a class of two-component scalar field models in a (1+1) Minkowskian space-time which generalize the well-known Montonen-Sarker-TrullingerBishop -hence MSTBmodel. This class includes all the field models whose static field equations are equivalent to the Newton equations of two-dimensional type I Liouville mechanical systems with a discrete set of insta...

On real generalized Ja obian varieties