A semi-numerical algorithm for the homology lattice and periods of complex elliptic surfaces over P1

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Symbolic Computation Pub Date : 2024-07-08 DOI:10.1016/j.jsc.2024.102357

Eric Pichon-Pharabod

引用次数: 0

Abstract

We provide an algorithm for computing a basis of homology of elliptic surfaces over $P_{C}^{1}$ that is sufficiently explicit for integration of periods to be carried out. This allows the heuristic recovery of several algebraic invariants of the surface, notably the Néron–Severi lattice, the transcendental lattice, the Mordell–Weil group and the Mordell–Weil lattice. This algorithm comes with a SageMath implementation.

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P1< 上复椭圆曲面的同调晶格和周期的半数值算法

我们提供了一种计算 PC1 上椭圆曲面同调基础的算法，这种算法足够明确，可以进行周期积分。这样就可以启发式地恢复曲面的几个代数不变式，特别是内龙-塞维里网格、超越网格、莫德尔-韦尔群和莫德尔-韦尔网格。该算法附带 SageMath 实现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Symbolic Computation 工程技术-计算机：理论方法

CiteScore

2.10

自引率

14.30%

发文量

审稿时长

142 days

期刊介绍： An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects. It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.