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Okounkov bodies and geodesic rays in Kähler geoemtry

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Title: Okounkov bodies and geodesic rays in Kähler geoemtry
Authors: Witt Nyström, David
Issue Date: 10-May-2012
University: Göteborgs universitet. Naturvetenskapliga fakulteten
Institution: Department of Mathematical Sciences ; Institutionen för matematiska vetenskaper
Parts of work: David Witt Nyström, Transforming metrics on a line bundle to the Okounkov body, Preprint (2009) at, arXiv:0903.5167v1.

David Witt Nyström, Test configurations and Okounkov bodies, Preprint (2010) at, arXiv:1001.3286, to appear in Compositio Mathematica.

Julius Ross and David Witt Nyström, Analytic test configurations and geodesic rays, Preprint (2011) at, arXiv:1101.1612v2.
Date of Defence: 2012-06-08
Disputation: Fredagen den 8 maj 2012, kl. 13.13, Hörsal Euler, Institutionen för matematiska vetenskaper, Chalmers tvärgata 3.
Degree: Doctor of Philosophy
Publication type: Doctoral thesis
Keywords: Okounkov bodies
Kähler geometry
Legendre transform
Monge-Ampère operator
Abstract: 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. We show that this generalizes the classical Legendre transform in convex and toric geometry, and also Chebyshev constants in pluripotential theory. Our main result is that the integral of the difference of two transforms over the... more
ISBN: 978-91-628-8478-9
Appears in Collections:Doctoral Theses / Doktorsavhandlingar Institutionen för matematiska vetenskaper
Doctoral Theses from University of Gothenburg / Doktorsavhandlingar från Göteborgs universitet



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