计算光滑 3 折叠最小对数差异的加权炸裂次数约束

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2024-03-08 DOI:10.1017/s030500412400001x

SHIHOKO ISHII

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引用次数: 0

摘要

我们研究了由定义在代数闭域上的光滑 3 折叠和 "一般"${\Bbb R}$ -ideal组成的一对。我们证明，每个这样的对的最小对数差异（简称 "mld"）都是由最多两次加权炸开得到的素除数计算出来的。这一约束被视为穆斯塔法-中村猜想的加权炸毁版本。我们还证明，如果这一对的 mld 不小于 1，那么它最多通过一次加权炸毁来计算。因此，mld 的 ACC 对此类棋对成立。

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A bound of the number of weighted blow-ups to compute the minimal log discrepancy for smooth 3-folds

We study a pair consisting of a smooth 3-fold defined over an algebraically closed field and a “general”

${\Bbb R}$

-ideal. We show that the minimal log discrepancy (“mld” for short) of every such a pair is computed by a prime divisor obtained by at most two weighted blow-ups. This bound is regarded as a weighted blow-up version of Mustaţă–Nakamura’s conjecture. We also show that if the mld of such a pair is not less than 1, then it is computed by at most one weighted blow-up. As a consequence, ACC of mld holds for such pairs.

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来源期刊

Mathematical Proceedings of the Cambridge Philosophical Society 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.