TY - JOUR

T1 - On generators of ideals defining projective toric varieties

AU - Ogata, Shoetsu

AU - Nakagawa, Katsuyoshi

PY - 2002/12/1

Y1 - 2002/12/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s002290200252

DO - 10.1007/s002290200252

M3 - Article

AN - SCOPUS:0036999831

VL - 108

SP - 33

EP - 42

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 1

ER -