k-normality of weighted projective spaces

Abstract

It is known that a complete linear system on a projective variety in a projective space is generated from the linear system of the projective space by restriction if its degree is sufficiently large. We obtain a bound of degree of linear systems on weighted projective spaces when they are generated from those of the projective spaces. In particular, we show that a weighted projective 3-space embedded by a complete linear system is projectively normal. We treat more generally Q-factorial toric varieties with the Picard number one, and obtain the same bounds for them as those of weighted projective spaces.