Ls Algebras and Schubert Varieties - Chirivì, Rocco
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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.

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Produktbeschreibung
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.
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