三次四倍、Gushel-Mukai四倍及其相关K3曲面的显式计算

IF 0.7 4区数学 Q2 MATHEMATICS

Experimental Mathematics Pub Date : 2022-04-25 DOI:10.1080/10586458.2023.2184882

Giovanni Staglianò

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引用次数: 1

摘要

我们介绍了Macaulay2软件包SpecialFanoFourfolds的一些应用，这是一个用于处理Hodge-special cubic four - fold和Hodge-special Gushel- Mukai four - fold的软件包。特别是，我们展示了如何构建这种四倍的新示例，其中一些被证明是合理的。我们还描述了如何计算与三次或Gushel-Mukai四倍相关的K3曲面，这依赖于K3曲面的一些模空间的显式唯一性。

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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Explicit Computations with Cubic Fourfolds, Gushel–Mukai Fourfolds, and their Associated K3 Surfaces

We present some applications of the Macaulay2 software package SpecialFanoFourfolds, a package for working with Hodge-special cubic fourfolds and Hodge-special Gushel--Mukai fourfolds. In particular, we show how to construct new examples of such fourfolds, some of which turn out to be rational. We also describe how to calculate K3 surfaces associated with cubic or Gushel-Mukai fourfolds, which relies on an explicit unirationality of some moduli spaces of K3 surfaces.

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来源期刊

Experimental Mathematics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses. Experiment has always been, and increasingly is, an important method of mathematical discovery. (Gauss declared that his way of arriving at mathematical truths was "through systematic experimentation.") Yet this tends to be concealed by the tradition of presenting only elegant, fully developed, and rigorous results. Experimental Mathematics was founded in the belief that theory and experiment feed on each other, and that the mathematical community stands to benefit from a more complete exposure to the experimental process. The early sharing of insights increases the possibility that they will lead to theorems: An interesting conjecture is often formulated by a researcher who lacks the techniques to formalize a proof, while those who have the techniques at their fingertips have been looking elsewhere. Even when the person who had the initial insight goes on to find a proof, a discussion of the heuristic process can be of help, or at least of interest, to other researchers. There is value not only in the discovery itself, but also in the road that leads to it.