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Newton-Okounkov bodies on projective bundles over curves. (English) Zbl 1419.14011
This article studies Newton-Okounkov bodies on projective bundles over a smooth projective curve over an algebraically closed field of characteristic zero.
In particular, the author computes all Newton-Okounkov bodies of ratonal big classes with respect to linear flags compatible with the Harder-Narasimhan filtration of a vector bundle. Moreover, he characterizes semi-stable vector bundles on a curve in terms of Newton-Okounkov bodies.
MSC:
14C20 Divisors, linear systems, invertible sheaves
14H60 Vector bundles on curves and their moduli
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
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