naa a22 4500 510736637 CHVBK 20180411083012.0 cr unu---uuuuu 180411e20130301xx s 000 0 eng 10.1007/s13366-012-0091-9 doi (NATIONALLICENCE)springer-10.1007/s13366-012-0091-9 Tropical secant graphs of monomial curves [Elektronische Daten] [María Cueto, Shaowei Lin] The first secant variety of a projective monomial curve is a threefold with an action by a one-dimensional torus. Its tropicalization is a three-dimensional fan with a one-dimensional lineality space, so the tropical threefold is represented by a balanced graph. Our main result is an explicit construction of that graph. As a consequence, we obtain algorithms to effectively compute the multidegree and Chow polytope of an arbitrary projective monomial curve. This generalizes an earlier degree formula due to Ranestad. The combinatorics underlying our construction is rather delicate, and it is based on a refinement of the theory of geometric tropicalization due to Hacking, Keel and Tevelev. The Managing Editors, 2012 Monomial curves nationallicence Secant varieties nationallicence Resolution graphs nationallicence Tropical implicitization nationallicence Newton polytope nationallicence Cueto María Mathematics Department, Columbia University, MC 4403, 10027, New York, NY, USA aut Lin Shaowei Department of Mathematics, University of California, 94720, Berkeley, CA, USA aut Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer-Verlag 54/1(2013-03-01), 383-418 0138-4821 54:1<383 2013 54 13366 https://doi.org/10.1007/s13366-012-0091-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13366-012-0091-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cueto María Mathematics Department, Columbia University, MC 4403, 10027, New York, NY, USA aut NATIONALLICENCE 700 1- Lin Shaowei Department of Mathematics, University of California, 94720, Berkeley, CA, USA aut NATIONALLICENCE 773 0- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Springer-Verlag 54/1(2013-03-01), 383-418 0138-4821 54:1<383 2013 54 13366 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer