16 research outputs found

    Special lagrangian fibrations on flag variety F3F^3

    Full text link
    One constructs lagrangian fibrations on the flag variety F3F^3 and proves that the fibrations are special.Comment: 19 page

    Enumerative aspects of the Gross-Siebert program

    Get PDF
    We present enumerative aspects of the Gross-Siebert program in this introductory survey. After sketching the program's main themes and goals, we review the basic definitions and results of logarithmic and tropical geometry. We give examples and a proof for counting algebraic curves via tropical curves. To illustrate an application of tropical geometry and the Gross-Siebert program to mirror symmetry, we discuss the mirror symmetry of the projective plane.Comment: A version of these notes will appear as a chapter in an upcoming Fields Institute volume. 81 page

    SYZ mirror symmetry for hypertoric varieties

    Full text link
    We construct a Lagrangian torus fibration on a smooth hypertoric variety and a corresponding SYZ mirror variety using TT-duality and generating functions of open Gromov-Witten invariants. The variety is singular in general. We construct a resolution using the wall and chamber structure of the SYZ base.Comment: v_2: 31 pages, 5 figures, minor revision. To appear in Communications in Mathematical Physic

    A Note on Tropical Triangles in the Plane

    Get PDF
    We define transversal tropical triangles (affine and projective) and characterize them via six inequalities to be satisfied by the coordinates of the vertices. We prove that the vertices of a transversal tropical triangle are tropically independent and they tropically span a classical hexagon whose sides have slopes ∞, 0, 1. Using this classical hexagon, we determine a parameter space for transversal tropical triangles. The coordinates of the vertices of a transversal tropical triangle determine a tropically regular matrix. Triangulations of the tropical plane are obtained
    corecore