Kodai Mathematical Journal

k-normality of weighted projective spaces

Shoetsu Ogata

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.

Article information

Source
Kodai Math. J., Volume 28, Number 3 (2005), 519-524.

Dates
First available in Project Euclid: 12 December 2005

https://projecteuclid.org/euclid.kmj/1134397765

Digital Object Identifier
doi:10.2996/kmj/1134397765

Mathematical Reviews number (MathSciNet)
MR2194542

Zentralblatt MATH identifier
1102.14036

Citation

Ogata, Shoetsu. k -normality of weighted projective spaces. Kodai Math. J. 28 (2005), no. 3, 519--524. doi:10.2996/kmj/1134397765. https://projecteuclid.org/euclid.kmj/1134397765