Sökning: "Okounkov bodies"

Hittade 3 avhandlingar innehållade orden Okounkov bodies.

  1. 1. Multipoint Okounkov bodies

    Författare :Antonio Trusiani; Chalmers tekniska högskola; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Seshadri constant; Okounkov body; Projective manifold; symplectic packings; Kähler geometry; ample line bundle;

    Sammanfattning : During the nineties, the field medallist Okounkov found a way to associate to an ample line bundle L over an n−complex dimensional projective manifold X a convex body in Rn, now called Okounkov body ∆(L). The construction depends on the choice of a valuation centered at one point p∈X and it works even if L is a big line bundle. LÄS MER

  3. 2. Okounkov bodies and geodesic rays in Kähler geoemtry

    Författare :David Witt Nyström; Göteborgs universitet; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Okounkov bodies; Kähler geometry; Legendre transform; Monge-Ampère operator; Okounkov bodies;

    Sammanfattning : This thesis presents three papers dealing with questions in Kähler geometry. In the first paper we construct a transform, called the Chebyshev transform, which maps continuous hermitian metrics on a big line bundle to convex functions on the associated Okounkov body. LÄS MER

  4. 3. Multipoint Okounkov bodies, strong topology of ω-plurisubharmonic functions and Kähler-Einstein metrics with prescribed singularities

    Författare :Antonio Trusiani; Chalmers tekniska högskola; []
    Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; NATURVETENSKAP; NATURAL SCIENCES; Okounkov bodies; Seshadri constant; Kähler-Einstein metrics; Kähler Geometry; Canonical metrics; Fano manifolds; Pluripotential theory; Complex Monge-Ampère equations; Kähler packing;

    Sammanfattning : The most classical topic in Kähler Geometry is the study of Kähler-Einstein metrics as solution of complex Monge-Ampère equations. This thesis principally regards the investigation of a strong topology for ω-plurisubharmonic functions on a fixed compact Kähler manifold (X,ω), its connection with complex Monge-Ampère equations with prescribed singularities and the consequent study of singular Kähler-Einstein metrics. LÄS MER