• 제목/요약/키워드: Tropical Algebraic Variety

검색결과 3건 처리시간 0.014초

ON TROPICAL QUADRIC SURFACES

  • KIM, YONGGU
    • 호남수학학술지
    • /
    • 제28권1호
    • /
    • pp.83-111
    • /
    • 2006
  • After introducing Tropical Algebraic Varieties, we give a polyhedral description of tropical hypersurfaces. Using TOPCOM and GAP, we show that there exist 59 types of two dimensional tropical quadric surfaces. We also show a criterion for a quadric hypersurface to be non-degenerate in terms of a tropical rank.

  • PDF

A NATURAL TOPOLOGICAL MANIFOLD STRUCTURE OF PHASE TROPICAL HYPERSURFACES

  • Kim, Young Rock;Nisse, Mounir
    • 대한수학회지
    • /
    • 제58권2호
    • /
    • pp.451-471
    • /
    • 2021
  • First, we define phase tropical hypersurfaces in terms of a degeneration data of smooth complex algebraic hypersurfaces in (ℂ∗)n. Next, we prove that complex hyperplanes are homeomorphic to their degeneration called phase tropical hyperplanes. More generally, using Mikhalkin's decomposition into pairs-of-pants of smooth algebraic hypersurfaces, we show that a phase tropical hypersurface with smooth tropicalization is naturally a topological manifold. Moreover, we prove that a phase tropical hypersurface is naturally homeomorphic to a symplectic manifold.

열대곡선 헤아리기 (Enumerate tropical algebraic curves)

  • 김영록;신용수
    • 한국수학사학회지
    • /
    • 제30권3호
    • /
    • pp.185-199
    • /
    • 2017
  • In tropical geometry, the sum of two numbers is defined as the minimum, and the multiplication as the sum. As a way to build tropical plane curves, we could use Newton polygons or amoebas. We study one method to convert the representation of an algebraic variety from an image of a rational map to the zero set of some multivariate polynomials. Mikhalkin proved that complex curves can be replaced by tropical curves, and induced a combination formula which counts the number of tropical curves in complex projective plane. In this paper, we present close examinations of this particular combination formula.