LS algebras and Schubert varieties

This thesis is essentially about the standard monomial theory.

It deals with Hodge algebras, doset algebras and LS algebras.

If Hodge algebras have a module basis given by the linearly ordered monomials from a poset structure, LS algebras have a module basis combinatorically described by the LS paths over a poset with bonds.

Some relations for LS paths monomials in the coordinate ring of (the cone over) a Schubert variety are known.

Our main result is that any Schubert variety admits a flat degeneration to a union of normal toric varieties.