1,720,975 research outputs found
Seshadri stratifications and standard monomial theory
Full text linkWe introduce the notion of a Seshadri stratification on an embedded projective variety. Such a structure enables us to construct a Newton-Okounkov simplicial complex and a flat degeneration of the projective variety into a union of toric varieties. We show that the Seshadri stratification provides a geometric setup for a standard monomial theory. In this framework, Lakshmibai-Seshadri paths for Schubert varieties get a geometric interpretation as successive vanishing orders of regular functions
On normal Seshadri stratifications
No full textThe existence of a Seshadri stratification on an embedded projective variety provides a flat degeneration of the variety to a union of projective toric varieties, called a semi-toric variety. Such a stratification is said to be normal when each irreducible component of the semi-toric variety is a normal toric variety. In this case, we show that a Gröbner basis of the defining ideal of the semi-toric variety can be lifted to define the embedded projective variety. Applications to Koszul and Gorenstein properties are discussed. Relations between LS-algebras and certain Seshadri stratifications are studied
Equations defining symmetric varieties and affine grassmannians
No full textSuppose σ be a simple involution of a semisimple algebraic group G, and suppose H is the subgroup of G of points fixed by σ. If the restricted root system is of type A,C, or BC and G is simply connected, or if the restricted root system is of type B and G is of adjoint type, then we describe a standard monomial theory and the equations for the coordinate ring k[G/H] using the standard monomial theory and the Plu ̈ cker relations of an appropriate (maybe infinite-dimensional) Grassmann variety
Equations Defining Symmetric Varieties and Affine Grassmannians
No full textSuppose sigma be a simple involution of a semisimple algebraic group G, and suppose H is the subgroup of G of points fixed by sigma. If the restricted root system is of type A, C, or BC and G is simply connected, or if the restricted root system is of type B and G is of adjoint type, then we describe a standard monomial theory and the equations for the coordinate ring k[G/H] using the standard monomial theory and the Plucker relations of an appropriate (maybe infinite-dimensional) Grassmann variety
LS algebras, valuations, and Schubert varieties
No full textIn this paper, we propose an algebraic approach via Lakshmibai–Seshadri (LS) algebras to establish a link between standard monomial theories, Newton–Okounkov bodies and valuations. This is applied to Schubert varieties, where this approach is compatible with the one using Seshadri stratifications in arXiv:2112.03776, showing that LS paths encode vanishing multiplicities with respect to the web of Schubert varieties
Seshadri stratifications and Schubert varieties: a geometric construction of a standard monomial theory
No full textA standard monomial theory for Schubert varieties is constructed exploiting (1) the geometry of the Seshadri stratifi-cations of Schubert varieties by their Schubert subvarieties and (2) the combinatorial LS-path character formula for Demazure modules. The general theory of Seshadri stratifications is improved by using arbitrary linearization of the partial order and by weak-ening the definition of balanced stratification
Degenerate flag varieties and Schubert varieties: A characteristic free approach
Full text linkWe consider the PBW filtrations over Z of the irreducible highest weight
modules in type An and Cn. We show that the associated graded modules can
be realized as Demazure modules for group schemes of the same type and
doubled rank. We deduce that the corresponding degenerate flag varieties
are isomorphic to Schubert varieties in any characteristic
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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