scholarly journals Equivalence of Mirror Families Constructed from Toric Degenerations of Flag Varieties

2008 ◽  
Vol 13 (1) ◽  
pp. 173-194 ◽  
Author(s):  
J. Rusinko
Author(s):  
Naoki Fujita ◽  
Akihiro Higashitani

Abstract A Newton–Okounkov body is a convex body constructed from a projective variety with a globally generated line bundle and with a higher rank valuation on the function field, which gives a systematic method of constructing toric degenerations of projective varieties. Its combinatorial properties heavily depend on the choice of a valuation, and it is a fundamental problem to relate Newton–Okounkov bodies associated with different kinds of valuations. In this paper, we address this problem for flag varieties using the framework of combinatorial mutations, which was introduced in the context of mirror symmetry for Fano manifolds. By applying iterated combinatorial mutations, we connect specific Newton–Okounkov bodies of flag varieties including string polytopes, Nakashima–Zelevinsky polytopes, and Feigin–Fourier–Littelmann–Vinberg polytopes.


Author(s):  
Xin Fang ◽  
Ghislain Fourier ◽  
Peter Littelmann

2020 ◽  
pp. 1-33
Author(s):  
Christopher Manon ◽  
Jihyeon Jessie Yang

Abstract We construct a family of compactifications of the affine cone of the Grassmannian variety of $2$ -planes. We show that both the tropical variety of the Plücker ideal and familiar valuations associated to the construction of Newton–Okounkov bodies for the Grassmannian variety can be recovered from these compactifications. In this way, we unite various perspectives for constructing toric degenerations of flag varieties.


Author(s):  
Lara Bossinger ◽  
Sara Lamboglia ◽  
Kalina Mincheva ◽  
Fatemeh Mohammadi

2021 ◽  
Vol 384 ◽  
pp. 107695
Author(s):  
Madeline Brandt ◽  
Christopher Eur ◽  
Leon Zhang
Keyword(s):  

2020 ◽  
Vol 224 (10) ◽  
pp. 106389
Author(s):  
Arpita Nayek ◽  
S.K. Pattanayak ◽  
Shivang Jindal

2020 ◽  
Vol 26 (2) ◽  
Author(s):  
Anders S. Buch ◽  
Sjuvon Chung ◽  
Changzheng Li ◽  
Leonardo C. Mihalcea

2017 ◽  
Vol 2 (2) ◽  
pp. 341-356 ◽  
Author(s):  
Nikita Karpenko
Keyword(s):  

Sign in / Sign up

Export Citation Format

Share Document