An algorithm for lifting points in a tropical variety

DOI10.1007/BF03191365zbMath1151.13021arXiv0705.2441MaRDI QIDQ934344

Thomas Markwig, Anders Nedergaard Jensen, Hannah Markwig

Publication date: 29 July 2008

Published in: Collectanea Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0705.2441

zbMATH Keywords

Puiseux seriestropical geometryPuiseux parametrization

Mathematics Subject Classification ID

Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Polyhedra and polytopes; regular figures, division of spaces (51M20) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Non-Archimedean valued fields (12J25) Computational aspects in algebraic geometry (14Q99) Affine geometry (14R99)

Related Items

Tropical geometry, the motivic nearby fiber, and limit mixed Hodge numbers of hypersurfaces, A note on tropical triangles in the plane, On the algebraicity of generalized power series, Computing tropical resultants, Universal valued fields and lifting points in local tropical varieties, Generic tropical varieties, Irreducibility criterion for algebroid curves, Beyond polyhedral homotopies, Formulas for monodromy, Tropical plane geometric constructions: a transfer technique in tropical geometry, The method of Gauss-Newton to compute power series solutions of polynomial homotopies, Tropical algebraic geometry in Maple: a preprocessing algorithm for finding common factors for multivariate polynomials with approximate coefficients, Positively hyperbolic varieties, tropicalization, and positroids, Complexity of deciding whether a tropical linear prevariety is a tropical variety, PUISEUX POWER SERIES SOLUTIONS FOR SYSTEMS OF EQUATIONS, Computing Tropical Curves via Homotopy Continuation, Tropical resultants for curves and stable intersection, On real tropical bases and real tropical discriminants, A tropical toolkit, Standard bases in \(Kt_1,\ldots ,t_m[x_1,\ldots ,x_n^s\)], Tropical bases by regular projections, Fibers of tropicalization, The Combinatorics of Plane Curve Singularities

Uses Software

• SINGULAR
• Gfan

Cites Work

• Fibers of tropicalization
• Puiseux expansion for space curves
• The Caporaso-Harris formula and plane relative Gromov-Witten invariants in tropical geometry
• A tropical approach to secant dimensions
• Computing tropical varieties
• The algebraic closure of the power series field in positive characteristic
• Non-archimedean amoebas and tropical varieties
• The group law on a tropical elliptic curve
• Enumerative tropical algebraic geometry in ℝ²
• The tropical Grassmannian
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