20 citations · 55 across the 18 of their papers we have counts for
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Semi-toric degenerations of Richardson varieties arising from cluster structures on flag varieties
Naoki Fujita
A toric degeneration of an irreducible variety is a flat degeneration to an irreducible toric variety. In the case of a flag variety, its toric degeneration with desirable properti…
Newton-Okounkov polytopes of flag varieties and marked chain-order polytopes
Naoki Fujita
Marked chain-order polytopes are convex polytopes constructed from a marked poset, which give a discrete family relating a marked order polytope with a marked chain polytope. In th…
Fano and weak Fano Hessenberg varieties
Hiraku Abe, Naoki Fujita, Haozhi Zeng
Regular semisimple Hessenberg varieties are smooth subvarieties of the flag variety, and their examples contain the flag variety itself and the permutohedral variety which is a tor…
Polyhedral realizations of crystal bases and convex-geometric Demazure operators
Naoki Fujita
The main object in this paper is a certain rational convex polytope whose lattice points give a polyhedral realization of a highest weight crystal basis. This is also identical to…
Algebraic and geometric properties of flag Bott-Samelson varieties and applications to representations
Naoki Fujita, Eunjeong Lee, Dong Youp Suh
We introduce the notion of flag Bott-Samelson variety as a generalization of Bott-Samelson variety and flag variety. Using a birational morphism from an appropriate Bott-Samelson v…
Geometry of regular Hessenberg varieties
Hiraku Abe, Naoki Fujita, Haozhi Zeng
Let be a complex semisimple Lie algebra. For a regular element in and a Hessenberg space , we consider a regular Hessenbe…
Folding procedure for Newton-Okounkov polytopes of Schubert varieties
Naoki Fujita
The theory of Newton-Okounkov polytopes is a generalization of that of Newton polytopes for toric varieties, and it gives a systematic method of constructing toric degenerations of…
Khovanskii bases of Cox-Nagata rings and tropical geometry
Martha Bernal, Daniel Corey, Maria Donten-Bury +2
The Cox ring of a del Pezzo surface of degree 3 has a distinguished set of 27 minimal generators. We investigate conditions under which the initial forms of these generators genera…
A comparison of Newton-Okounkov polytopes of Schubert varieties
Naoki Fujita, Hironori Oya
A Newton-Okounkov body is a convex body constructed from a polarized variety with a valuation on its function field. Kaveh (resp., the first author and Naito) proved that the Newto…