On quadratic generation of ideals defining projective toric varieties

Abstract

For any ample line bundle $L$ on a projective toric variety of dimension $n$, it is known that the line bundle $L^{\otimes i}$ is normally generated if $i$ is greater than or equal to $n-1$. We prove that $L^{\otimes i}$ is also normally presented if $i$ is greater than or equal to $n-1$. Furthermore we show that $L^{\otimes i}$ is normally presented for $i\ge [n/2]+1$ if $L$ is normally generated.