有界体积算子与有界负性
Bounded volume denominators and bounded negativity
摘要：
本文研究了光滑射影曲面上大线丛体积中的扩张子是否有界的问题。特别是，我们研究了这个条件如何与有界负性（即，不可约曲线的自相交的有界性）。我们的第一个结果表明，有界的体积膨胀剂是等价的\emph{primitive bounded negativity}，这反过来是由有界的负性。我们将这个结果与因子的半有效阶的研究联系起来：我们的第二个结果表明，只有在取任意大的倍数后，负类才有效。
英文摘要：
In this paper we study the question of whether on smooth projective surfaces the denominators in the volumes of big line bundles are bounded. In particular we investigate how this condition is related to bounded negativity (i.e., the boundedness of self-intersections of irreducible curves). Our first result shows that boundedness of volume denominators is equivalent to \emph{primitive bounded negativity}, which in turn is implied by bounded negativity. We connect this result to the study of semi-effective orders of divisors: Our second result shows that negative classes exist that become effective only after taking an arbitrarily large multiple.
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