On generators of ideals defining projective toric varieties

Shoetsu Ogata, Katsuyoshi Nakagawa

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

For any ample line bundle L on a projective toric variety of dimension n, it is proved that the line bundle L⊗i is normally generated if i is greater than or equal to n - 1, and examples showing that this estimate is best possible are given. Moreover we prove an estimate for the degree of the generators of the ideals defining projective toric varieties. In particular, when L is normally generated, the defining ideal of the variety embedded by the global sections of L has generators of degree at most n + 1. When the variety is embedded by the global sections of L⊗(n-1), then the defining ideal has generators of degree at most three.

Original languageEnglish
Pages (from-to)33-42
Number of pages10
Journalmanuscripta mathematica
Volume108
Issue number1
DOIs
Publication statusPublished - 2002 Dec 1

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'On generators of ideals defining projective toric varieties'. Together they form a unique fingerprint.

Cite this