Department of Mathematics and Physics, University of Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany
Abstract:
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.