Computing toric degenerations of grassmannians and flag varieties arising from tropical geometry
- Autores: Fatemeh Mohammadi
- Localización: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 1132-6360, Nº. 43, 2018 (Ejemplar dedicado a: Proceedings of the XVI EACA Zaragoza Encuentros de Algebra Computacional y Aplicaciones), págs. 19-19
- Idioma: inglés
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Resumen
A toric variety is a certain algebraic variety modeled on a convex polyhedron. Toric varieties play an important role in commutative algebra. I give an overview talk on toric degenerations of flag varieties and Grassmannians arising from tropical geometry and representation theory. I will compare toric degenerations arising from string polytopes with those obtained from tropical cones of flag varieties and will explain how the corresponding toric polytopes can be seen as Newton-Okounkov bodies for the valuations associated to each tropical cone. I will also present the necessary condition to obtain a toric initial ideal of Grassmannian of 3-planes explaining computational challenges around this problem. This is based on joint works with Kristin Shaw and with Lara Bossinger, Sara Lamboglia, and Kalina Mincheva.
