The diminished base locus is not always closed
The diminished base locus is not always closed
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减少的碱基轨迹并不总是闭合的
DOI：
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发表时间：
2012
影响因子：
1.8
通讯作者：
John Lesieutre
中科院分区：
文献类型：
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作者：
John Lesieutre
摘要我们在闭合可动锥上的${mathbb{P}}^{3}$的9个非常一般的点上证明了一个伪有效的$mathbb{R}$-除数${D}_{lambda}$，这些点与一组曲线的并集为Zariski密的负交。由此可见，减小碱基轨迹${oldsymbol{B}}_{-}({D}_{lambda})={igcup}_{A, ext{ample}} oldsymbol{B}({D}_{lambda}+A)$是不闭合的，并且${D}_{lambda}$即使在非常弱的意义上也不允许Zariski分解。通过类似的方法，我们在${mathbb{P}}^{2}$的10个不同点的膨胀族上构造一个$mathbb{R}$-除数，它在非常一般的纤维上是nef，但在基数上的可数素数除数上不能是nef。
Abstract We exhibit a pseudoeffective $mathbb{R}$-divisor ${D}_{lambda }$ on the blow-up of ${mathbb{P}}^{3}$ at nine very general points which lies in the closed movable cone and has negative intersections with a set of curves whose union is Zariski dense. It follows that the diminished base locus ${oldsymbol{B}}_{-}({D}_{lambda })={igcup }_{A, ext{ample}}oldsymbol{B}({D}_{lambda }+A)$ is not closed and that ${D}_{lambda }$ does not admit a Zariski decomposition in even a very weak sense. By a similar method, we construct an $mathbb{R}$-divisor on the family of blow-ups of ${mathbb{P}}^{2}$ at ten distinct points, which is nef on a very general fiber but fails to be nef over countably many prime divisors in the base.