Kodai Mathematical Journal

On quadratic generation of ideals defining projective toric varieties

Shoetsu Ogata

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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.

Article information

Source
Kodai Math. J., Volume 26, Number 2 (2003), 137-146.

Dates
First available in Project Euclid: 26 August 2003

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1061901058

Digital Object Identifier
doi:10.2996/kmj/1061901058

Mathematical Reviews number (MathSciNet)
MR2004f:14075

Zentralblatt MATH identifier
1071.14055

Citation

Ogata, Shoetsu. On quadratic generation of ideals defining projective toric varieties. Kodai Math. J. 26 (2003), no. 2, 137--146. doi:10.2996/kmj/1061901058. https://projecteuclid.org/euclid.kmj/1061901058


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