Combinatorial commutative algebra is an active area of research with thriving connections to
other fields of pure and applied mathematics. This book provides a self-contained …

Let G be a simply connected semisimple complex algebraic group. We prove that every
Schubert variety of G has a flat degeneration into a toric variety. This provides a …

We prove that any affine, resp. polarized projective, spherical variety admits a flat
degeneration to an affine, resp. polarized projective, toric variety. Motivated by mirror …

This note constructs the flat toric degeneration of the manifold F ℓ n of flags in C n due to
Gonciulea and Lakshmibai (Transform. Groups 1 (3)(1996) 215) as an explicit GIT quotient …

While the projections of Schubert varieties in a full generalized flag manifold G/B to a partial
flag manifold G/P are again Schubert varieties, the projections of Richardson varieties …

This book provides an introduction to flag varieties and their Schubert subvarieties. The
book portrays flag varieties as an interplay of algebraic geometry, algebraic groups …

Following the historical track in pursuing $ T $-equivariant flat toric degenerations of flag
varieties and spherical varieties, we explain how powerful tools in algebraic geometry and …

The theory of Seshadri stratifications has been developed by the authors with the intention to
build up a new geometric approach towards a standard monomial theory for embedded …

We 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 …

This monograph represents an expanded version of a series of lectures given by V.
Lakshmibai on Grassmannian varieties at the workshop on “Geometric Representation …