Universität zu Köln

Müller, Henrik (2024). Multiprojective Seshadri stratifications for Schubert varieties and standard monomial theory. PhD thesis, Universität zu Köln.

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Abstract

Via normal Seshadri stratifications, Chirivì, Fang and Littelmann obtained a standard monomial theory (SMT) on the homogeneous coordinate ring of certain embedded projective varieties, that is to say a basis of so called standard monomials. In the case of Schubert varieties such a SMT was already developed combinatorially by Lakshmibai, Musili and Seshadri. We generalize the notion of a Seshadri stratification to closed subvarieties in a product of projective spaces and construct such stratifications on Schubert varieties in every Dynkin type. Using the Littelmann path model, we show that these stratifications provide a geometric explanation of the SMT of Hodge and Young indexed by semistandard Young tableaux, the SMT of Lakshmibai, Musili and Seshadri and more general, of a SMT indexed by sequences of LS-paths.