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From standard monomial theory to semi-toric degenerations via Newton-Okounkov bodies


Authors: X. Fang and P. Littelmann
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 78 (2017), vypusk 2.
Journal: Trans. Moscow Math. Soc. 2017, 275-297
MSC (2010): Primary 14M15; Secondary 14M25, 52B20
DOI: https://doi.org/10.1090/mosc/273
Published electronically: December 1, 2017
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Abstract: The Hodge algebra structures on the homogeneous coordinate rings of Grassmann varieties provide semi-toric degenerations of these varieties. In this paper we construct these semi-toric degenerations using quasi-valuations and triangulations of Newton-Okounkov bodies.


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Additional Information

X. Fang
Affiliation: Mathematisches Institut, Universität zu Köln, Cologne, Germany
Email: xfang@math.uni-koeln.de

P. Littelmann
Affiliation: Mathematisches Institut, Universität zu Köln, Cologne, Germany
Email: peter.littelmann@math.uni-koeln.de

DOI: https://doi.org/10.1090/mosc/273
Keywords: Distributive lattice, Hibi variety, standard monomial theory, toric degeneration, Newton--Okounkov body, Grassmann variety
Published electronically: December 1, 2017
Dedicated: Dedicated to Ernest Vinberg on the occasion of his 80th birthday
Article copyright: © Copyright 2017 X.Fang, P.Littelmann

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