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arXiv math/0009122math.AG
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关于邻接丛不张成的低次极化曲面

On polarized surfaces of low degree whose adjont bundles are not spanned

Gian Mario Besana, Sandra Di Rocco

摘要:

光滑复杂的表面极化的充分和全球产生的线丛的程度三,四,使伴随丛不是全球产生的,被认为是。在平滑曲线上的向量丛的滚动被示出为三阶的唯一示例。两类的例子在度四,其中之一示出的特征经常这样的对。一个里德型定理,其中的偏振度的假设被删除。

英文摘要:

Smooth complex surfaces polarized with an ample and globally generated line bundle of degree three and four, such that the adjoint bundle is not globally generated, are considered. Scrolls of a vector bundle over a smooth curve are shown to be the only examples in degree three. Two classes of examples in degree four are presented, one of which is shown to characterize regular such pairs. A Reider-type theorem is obtained in which the assumption on the degree of the polarization is removed.

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