ar X iv : 0 70 6 . 41 78 v 3 [ m at h . C O ] 1 3 Ja n 20 09 Lattice Polytopes of Degree 2
نویسندگان
چکیده
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.
منابع مشابه
ar X iv : 0 70 6 . 41 78 v 1 [ m at h . C O ] 2 8 Ju n 20 07 Lattice polytopes of degree 2 Jaron Treutlein
Abstract. A theorem of Scott gives an upper bound for the normalized volume of lattice polygons with exactly i > 0 interior lattice points. We give a new proof for this theorem and classify polygons with maximal volume. Then we show that the same bound is true for the normalized volume of lattice polytopes of degree 2 even in higher dimension. From a theorem of Victor Batyrev the finiteness of ...
متن کاملar X iv : 0 70 6 . 41 78 v 2 [ m at h . C O ] 2 1 Fe b 20 08 Lattice Polytopes of Degree 2
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. The finiteness of lattice polytopes of degree 2 up to standard pyramids and affine unimodular transformation follows from a theore...
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