اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSymmetric crosscuts and tropical moduli
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We investigate geometric embeddings among several classes of stacky fans and algorithms, e.g., to compute their homology. Interesting cases arise from moduli spaces of tropical curves. Specifically, we study the embedding of the moduli of tropical honeycomb curves into the moduli of all tropical $K_4$-curves.
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We develop techniques for studying fundamental groups and integral singular homology of symmetric Delta-complexes, and apply these techniques to study moduli spaces of stable tropical curves of unit volume, with and without marked points. As one appl
ication, we show that Delta_g and Delta_{g,n} are simply connected, for positive g. We also show that Delta_3 is homotopy equivalent to the 5-sphere, and that Delta_4 has 3-torsion in H_5.
We show that the number of combinatorial types of clusters of type $D_4$ modulo reflection-rotation is exactly equal to the number of combinatorial types of tropical planes in $mathbb{TP}^5$. This follows from a result of Sturmfels and Speyer which c
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We study the combinatorics of tropical hyperplane arrangements, and their relationship to (classical) hyperplane face monoids. We show that the refinement operation on the faces of a tropical hyperplane arrangement, introduced by Ardila and Develin i
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We report on a recent implementation of patchworking and real tropical hypersurfaces in $texttt{polymake}$. As a new mathematical contribution we provide a census of Betti numbers of real tropical surfaces.
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