复杂投影超曲面的有效同调与周期

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Mathematics of Computation Pub Date : 2024-02-07 DOI:10.1090/mcom/3947

Pierre Lairez, Eric Pichon-Pharabod, Pierre Vanhove

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引用次数: 0

摘要

我们介绍了一种计算光滑复射超曲面周期的新算法。该算法与计算超曲面奇异同调的明确基础的新方法相互交织。它基于 Picard-Lefchetsz 理论，依赖于计算超平面截面的单参数族对给定截面同调引起的单色作用。我们提供了一个 SageMath 实现。例如，在笔记本电脑上，它可以在通常一个小时内计算出数百位精度的光滑复曲面的周期。

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Effective homology and periods of complex projective hypersurfaces

We introduce a new algorithm for computing the periods of a smooth complex projective hypersurface. The algorithm intertwines with a new method for computing an explicit basis of the singular homology of the hypersurface. It is based on Picard–Lefschetz theory and relies on the computation of the monodromy action induced by a one-parameter family of hyperplane sections on the homology of a given section.

We provide a SageMath implementation. For example, on a laptop, it makes it possible to compute the periods of a smooth complex quartic surface with hundreds of digits of precision in typically an hour.

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来源期刊

Mathematics of Computation 数学-应用数学

CiteScore

3.90

自引率

5.00%

发文量

审稿时长

7.0 months

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods. Articles must be of significant computational interest and contain original and substantial mathematical analysis or development of computational methodology.