Volume of line bundles via valuation vectors (different from Okounkov bodies)

2019/03/11 by Braunling, Oliver
#13F30 #14C20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.04317

Abstract

Up to a factor 1/n!, the volume of a big line bundle agrees with the Euclidean volume of its Okounkov body. The latter is the convex hull of top rank valuation vectors of sections, all with respect to a single flag. In this text we give a different volume formula, valid in the ample cone, also based on top rank valuation vectors, but mixing data along several different flags.

Related

• Volumes of line bundles
• Volumes of Arithmetic Okounkov Bodies
• On Volumes of Arithmetic Line Bundles II
• Intersection numbers as mixed volumes of Newton-Okounkov bodies
• On the volume of a line bundle