Laurent determinants and arrangements of hyperplane amoebas

By M. Forsberg, Mikael Passare, A. Tsikh. 2000

196 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/516effb729c4980932ab5724196ec683ebec3163

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Real algebraic curves, the moment map and amoebas (2000, background): “[3] obtained the following upper bound for this number in terms of ∆.”
A tropical approach to enumerative geometry (2006, background): “Amoebas of complex algebraic hypersurfaces were introduced in [7] and studied further in [6, 8, 15, 16, 17, 20, 21].”
Decomposition into pairs-of-pants for complex algebraic hypersurfaces (2002, background): “By [3] this component is contained in the component of R rAt corresponding to the index k.”
Amoebas of Algebraic Varieties and Tropical Geometry (2004, background): “be the Newton polyhedron of f. Theorem 1.8 (Forsberg-Passare-Tsikh [ 10 ]).”
Amoebas, nonnegative polynomials and sums of squares supported on circuits (2014, background): “having their nature in complex algebraic geometry with applications in various mathematical subjects including complex analysis [10,11], the topology of real algebraic curves [24], dynamical systems [8], dimers/crystal shapes [18], and in particular with strong connections to tropical geometry, see ”
Patchworking singular algebraic curves, non-Archimedean amoebas and enumerative geometry (2002, background): “ng conditions. 1 Non-Archimedean amoebas 1.1 Preliminaries Amoebas of complex algebraic hypersurfaces have been introduced in [6]. Geometry of such amoebas and their applications have been studied in [5, 6, 7, 13, 14, 15, 18, 19]. We are interested in “non-Archimedean amoebas”, i.e., deﬁned over ﬁel”
Amoebas, Monge-Ampère measures, and triangulations of the Newton polytope. (2004, unknown): “In [4] Forsberg, Passare, and Tsikh defined the order of such a component to be the vector ν = (ν 1 , . . . , ν n ) given by the formula ν j = 1 (2πi) n Log −1 (x) ∂ f ∂z j z j dz 1 · · · dz n f (z)z 1 · · · z n , x ∈ E. (2) Here x may be any point in E.”
Linear independence over tropical semirings and beyond (2008, background): “... structures have appeared in relation with in a variety of fields, like operations research and optimization [Vor67, CG79, GM08b], discrete event systems [BCOQ92, CGQ99], automata theory (see [Pin98] and its references), quasi-classic asymptotics [Mas87], Hamilton-Jacobi partial differential equa”