Negative curves on algebraic surfaces
Negative curves on algebraic surfaces
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代数曲面上的负曲线
DOI：
10.1215/00127094-2335368
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发表时间：
2011
影响因子：
2.5
通讯作者：
T. Szemberg
中科院分区：
文献类型：
--
作者：
Thomas Bauer;B. Harbourne;A. L. Knutsen;A. Küronya;S. Müller–Stach;X. Roulleau;T. Szemberg
研究了代数曲面上的负自交曲线。我们的主要结果表明，存在光滑复射影曲面X，与Hilbert模曲面有关，使得X包含任意负自相交C2的约化的不可约曲线C.以前唯一已知的例子表面，其中C2是没有限制低于是在积极的特点，和一般的期望是，没有例子可以出现在复杂的数字。事实上，我们表明，在积极的特点的例子的想法不能产生的例子在复数域，因此我们的复杂的例子需要一个不同的方法。
We study curves of negative self-intersection on algebraic surfaces. Our main result shows there exist smooth complex projective surfaces X, related to Hilbert modular surfaces, such that X contains reduced, irreducible curves C of arbitrarily negative self-intersection C 2 . Previously the only known examples of surfaces for which C 2 was not bounded below were in positive characteristic, and the general expectation was that no examples could arise over the complex numbers. Indeed, we show that the idea underlying the examples in positive characteristic cannot produce examples over the complex number field, and thus our complex examples require a different approach.