Complex Analysis and Algebraic Geometry: Defining Equations for Certain Types of Polarized Varieties
Complex Analysis and Algebraic Geometry: Defining Equations for Certain Types of Polarized Varieties
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复分析和代数几何：定义某些类型的极化品种的方程
DOI：
10.1017/cbo9780511569197.013
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
T. Fujita
中科院分区：
文献类型：
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作者：
T. Fujita
本文改进了Mumford[5]的一个结果。明确地说，我们修正了我们的符号和术语。设每个簇都定义在代数闭域K上，对于一个簇V上的线丛L，M，我们用R(L，M)表示它是自然乘法同态→F(L+M)的核。如果г(TL)F(L)→T((t+1)L)对每个t≥1是满射，则称V上的线丛是单生成的。如果L是单生成的，且如果自然同态R(SL，TL)>；T(L)→R(SL，(t+1)L)对所有的S，t≥12都是满射，则称其是二次表示的
In this paper we improve a result of Mumford [5]. To be explicit, we fix our notation and terminology". Every variety is assumed to be defined over an algebraically closed field K. For line bundles L, M on a variety V we denote by R (L, M) the kernel of the natural multiplication homomorphism Ã'(L)® Ã (M)→ F (L+ M). A line bundle L on V is said to be simply generated if г (tL) F (L)→ T ((t+ 1) L) is surjective for every t≥ 1. L is said to be quadratically presented if it is simply generated and if the natural homomorphism R (sL, tL)> T (L)→ R (sL,(t+ 1) L) is surjective for all s, t≥ 12. Now we state the following