2015/10/02 by David Witt Nyström, Nyström, David Witt
Mathematics · #14C20 #14C30 #32Q15 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:14C20 #msc:14C30 #msc:32Q15
paper · pdf · doi:10.48550/arxiv.1510.00510
13 pages. New version introduces the notion of Okounkov domain and considers Kähler embeddings of domains with their standard Kähler structure
arxiv created 2015/12/22 · arxiv updated 2015/12/23
Given a projective manifold X equipped with an ample line bundle L, we show how to embed certain torus-invariant domains D ⊆ℂn into X so that the Euclidean Kähler form on D extends to a Kähler form on X lying in the first Chern class of L. This is done using Okounkov bodies Δ(L), and the image of D under the standard moment map will approximate Δ(L). This means that the volume of D can be made to approximate the Kähler volume of X arbitrarily well. As a special case we can let D be an ellipsoid. We also have similar results when L is just big.