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Award ID contains: 2001739

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  1. ; (, Advances in Geometry)
    Abstract We study Dressians of matroids using the initial matroids of Dress and Wenzel. These correspond to cells in regular matroid subdivisions of matroid polytopes. An efficient algorithm for computing Dressians is presented, and its implementation is applied to a range of interesting matroids. We give counterexamples to a few plausible statements about matroid subdivisions. 
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  2. ; (, Transactions of the American Mathematical Society, Series B)
    We show that the non-Archimedean skeleton of the d d -th symmetric power of a smooth projective algebraic curve X X is naturally isomorphic to the d d -th symmetric power of the tropical curve that arises as the non-Archimedean skeleton of X X . The retraction to the skeleton is precisely the specialization map for divisors. Moreover, we show that the process of tropicalization naturally commutes with the diagonal morphisms and the Abel-Jacobi map and we exhibit a faithful tropicalization for symmetric powers of curves. Finally, we prove a version of the Bieri-Groves Theorem that allows us, under certain tropical genericity assumptions, to deduce a new tropical Riemann-Roch-Theorem for the tropicalization of linear systems. 
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  3. ; (, Michigan Mathematical Journal)
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  4. ; ; (, Advances in Mathematics)
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  5. (, Le Matematiche)
    Accepted Manuscript Full Text Available