Max Glick - On singularity confinement for the pentagram map

dmtcs:3049 - Discrete Mathematics & Theoretical Computer Science, January 1, 2012, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) - https://doi.org/10.46298/dmtcs.3049
On singularity confinement for the pentagram map

Authors: Max Glick

    The pentagram map, introduced by R. Schwartz, is a birational map on the configuration space of polygons in the projective plane. We study the singularities of the iterates of the pentagram map. We show that a ``typical'' singularity disappears after a finite number of iterations, a confinement phenomenon first discovered by Schwartz. We provide a method to bypass such a singular patch by directly constructing the first subsequent iterate that is well-defined on the singular locus under consideration. The key ingredient of this construction is the notion of a decorated (twisted) polygon, and the extension of the pentagram map to the corresponding decorated configuration space.


    Volume: DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)
    Section: Proceedings
    Published on: January 1, 2012
    Imported on: January 31, 2017
    Keywords: pentagram map, singularity confinement, decorated polygon,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
    Fundings :
      Source : OpenAIRE Research Graph
    • Algebraic Combinatorics; Funder: National Science Foundation; Code: 1101152
    • EMSW21-RTG: Developing American Research Leadership in Algebraic Geometry and its Boundaries; Funder: National Science Foundation; Code: 0943832

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