Announcements of new results
We construct a countable chain of Boolean semilattices, with all inclusion maps preserving the join and the bounds, whose union cannot be represented as the maximal semilattice quotient of the positive cone of any dimension group. We also construct a similar example with a countable chain of strongly distributive bounded semilattices. This solves a problem of F. Wehrung.
Using the polytopes defined in an earlier paper, we show in this paper the existence of degeneration of a large class of Schubert varieties of to toric varieties by extending the method used by Gonciulea and Lakshmibai for a miniscule to Schubert varieties in .