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Titlebook: Combinatorial Algebraic Geometry; Selected Papers From Gregory G. Smith,Bernd Sturmfels Book 2017 Springer Science+Business Media LLC 2017

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From Curves to Tropical Jacobians and Back,calize the curve and then use the weighted metric graph to compute the tropical Jacobian. Finding the abstract tropicalization of a general curve defined by polynomial equations is difficult, because an embedded tropicalization may not be faithful, and there is no known algorithm for carrying out se
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Secants, Bitangents, and Their Congruences, of all lines which intersect .. We compute the singular locus of this hypersurface, which contains the congruence of all secants to .. A surface . in . defines the Hurwitz hypersurface in . of all lines which are tangent to .. We show that its singular locus has two components for general enough .:
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,Khovanskii Bases of Cox–Nagata Rings and Tropical Geometry,rms of these generators generate the initial algebra of this Cox ring. Sturmfels and Xu provide a classification in the case of degree 4 del Pezzo surfaces by subdividing the tropical Grassmannian .. After providing the necessary background on Cox–Nagata rings and Khovanskii bases, we review the cla
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Equations and Tropicalization of Enriques Surfaces,mpute the tropical homology, thus recovering a special case of the result of [.], and establish a connection between the dimension of the tropical homology groups and the Hodge numbers of the corresponding algebraic Enriques surface.
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