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arXiv · 1903.04317

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

Oliver Braunling
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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.

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Oliver Braunling. 2019-03-11. Volume of line bundles via valuation vectors (different from Okounkov bodies). https://arxiv.org/abs/1903.04317

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