Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory

@article{Kaveh2009NewtonOkounkovBS,
title={Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory},
author={Kiumars Kaveh and Askold Khovanskii},
journal={arXiv: Algebraic Geometry},
year={2009}
}
• Published 21 April 2009
• Mathematics
• arXiv: Algebraic Geometry
Generalizing the notion of Newton polytope, we define the Newton-Okounkov body, respectively, for semigroups of integral points, graded algebras, and linear series on varieties. We prove that any semigroup in the lattice Z^n is asymptotically approximated by the semigroup of all the points in a sublattice and lying in a convex cone. Applying this we obtain several results: we show that for a large class of graded algebras, the Hilbert functions have polynomial growth and their growth…
245 Citations
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