Newton polytopes and tropical geometry

B. Ya. Kazarnovskii   ; A. G. Khovanskii   ; A. I. Esterov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 76 (2021) no. 1, pp. 91-175

Résumé

The practice of bringing together the concepts of ‘Newton polytopes’, ‘toric varieties’, ‘tropical geometry’, and ‘Gröbner bases’ has led to the formation of stable and mutually beneficial connections between algebraic geometry and convex geometry. This survey is devoted to the current state of the area of mathematics that describes the interaction and applications of these concepts. Bibliography: 68 titles.

Détail

Keywords: family of algebraic varieties, Newton polytope, ring of conditions, toric variety, tropical geometry, mixed volume, exponential sum.

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