Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Newton-Okounkov bodies, semigroups of integral points, graded algebras
  and intersection theory   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 coefficients satisfy a Brunn-Minkowski type
inequality. We prove analogues of Fujita approximation theorem for semigroups
of integral points and graded algebras, which imply a generalization of this
theorem for arbitrary linear series. Applications to intersection theory
include a far-reaching generalization of the Kushnirenko theorem (from Newton
polytope theory) and a new version of the Hodge inequality. We also give
elementary proofs of the Alexandrov-Fenchel inequality in convex geometry and
its analogue in algebraic geometry.

24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat