Lattice polytopes of degree 2

Jaron Treutlein

Published 2007-06-28, updated 2009-01-13Version 3

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.