Lattice polytopes of degree 2

Details Lattice polytopes of degree 2 Lattice polytopes of degree 2

2007-06-28

arxiv.org/abs/0706.4178v3

Mathematics

Combinatorics

8 pages

Scientific paper

A theorem of Scott gives an upper bound for the normalized volume of lattice polygons with exactly $i>0$ interior lattice points. We will show that the same bound is true for the normalized volume of lattice polytopes of degree 2 even in higher dimensions. In particular, there is only a finite number of quadratic polynomials with fixed leading coefficient being the $h^*$-polynomial of a lattice polytope.

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