From the sixteenth Hilbert problem to tropical geometry

DOI10.1007/s11537-008-0832-6zbMath1185.14053OpenAlexW1992224331MaRDI QIDQ1043879

O. Ya. Viro

Publication date: 9 December 2009

Published in: Japanese Journal of Mathematics. 3rd Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11537-008-0832-6

zbMATH Keywords

patchworkreal algebraic curveidempotent mathematicstropical geometrysixteenth Hilbert problem

Mathematics Subject Classification ID

Enumerative problems (combinatorial problems) in algebraic geometry (14N10) Topology of real algebraic varieties (14P25)

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Cites Work

• Classification of flexible \(M\)-curves of degree 8 up to isotopy
• Classification of nonsingular surfaces of degree 4 in \({\mathbb{R}}{\mathbb{P}}^ 3\) with respect to rigid isotopies
• The complex separation of real surfaces and extensions of Rokhlin congruence
• Counting curves via lattice paths in polygons
• Patchworking algebraic curves disproves the Ragsdale conjecture
• Progress in the topology of real algebraic varieties over the last six years
• Centennial History of Hilbert's 16th Problem
• Enumerative tropical algebraic geometry in ℝ²
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