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Computing toric degenerations of flag varieties. (English) Zbl 1390.14194
Smith, Gregory G. (ed.) et al., Combinatorial algebraic geometry. Selected papers from the 2016 apprenticeship program, Ottawa, Canada, July–December 2016. Toronto: The Fields Institute for Research in the Mathematical Sciences; New York, NY: Springer (ISBN 978-1-4939-7485-6/hbk; 978-1-4939-7486-3/ebook). Fields Institute Communications 80, 247-281 (2017).
Summary: We compute toric degenerations arising from the tropicalization of the full flag varieties \(\text{Fl}_4\) and \(\text{Fl}_5\) embedded in a product of Grassmannians. For \(\text{Fl}_4\) and \(\text{Fl}_5\) we compare toric degenerations arising from string polytopes and the FFLV polytope with those obtained from the tropicalization of the flag varieties. We also present a general procedure to find toric degenerations in the cases where the initial ideal arising from a cone of the tropicalization of a variety is not prime.
For the entire collection see [Zbl 1387.14014].

MSC:
14T05 Tropical geometry (MSC2010)
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14M15 Grassmannians, Schubert varieties, flag manifolds
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
Software:
Macaulay2
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