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arXiv 1011.0979math.AG
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关于伴随线丛的Seshadri常数

On the Seshadri constants of adjoint line bundles

Thomas Bauer, Tomasz Szemberg

摘要:

在本文中,我们关注的Seshadri常数的可能值。虽然在一般情况下,每一个正有理数出现的地方Seshadri常数的一些丰富的线丛,我们指出,伴随线丛有明确的下界只取决于尺寸的基础品种。在表面的情况下,最佳的下界是1/2,我们的特点是所有可能的值在1/2和1之间的范围内-有令人惊讶的是很少。正如预期的那样,人们得到了非常丰富的线丛的伴随的Seshadri常数的更严格的结果。在这种情况下,我们的边界情况下的描述利用表面上的双折射理论结果。最后,我们研究了多点情形下伴随线丛的Seshadri常数。

英文摘要:

In the present paper we are concerned with the possible values of Seshadri constants. While in general every positive rational number appears as the local Seshadri constant of some ample line bundle, we point out that for adjoint line bundles there are explicit lower bounds depending only on the dimension of the underlying variety. In the surface case, where the optimal lower bound is 1/2, we characterize all possible values in the range between 1/2 and 1 -- there are surprisingly few. As expected, one obtains even more restrictive results for the Seshadri constants of adjoints of very ample line bundles. Our description of the border case in this situation makes use of adjunction-theoretical results on surfaces. Finally, we study Seshadri constants of adjoint line bundles in the multi-point setting.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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