论文标题
网络由Del Pezzo表面和超置矩阵功能身份的网络
Webs by conics on del Pezzo surfaces and hyperlogarithmic functional identities
论文作者
论文摘要
对于$ d $从2到6不等，我们证明，圆锥网的网络自然在任何光滑的Del Pezzo表面上$ d $ $ d $都具有有趣的功能性身份，其组件的所有成分都是一定的反对称超对称性$ 7-D $。我们的方法相对于$ d $是统一的，最终依赖于Weyl组对所考虑的Del Pezzo表面中包含的一组线的作用的经典结果。这一系列的“ Del Pezzo的超块矩阵功能身份”是对著名且知识渊博的3-期和5-期身份的自然概括，该对数和dionogarithm（“ Abel的关系”）分别分别与$ d = 6 $和$ d = 5 $相对应。本文以包含几个问题和一些可能有趣的观点的部分结尾。
For $d$ ranging from 2 to 6, we prove that the web by conics naturally defined on any smooth del Pezzo surface of degree $d$ carries an interesting functional identity whose components all are a certain antisymmetric hyperlogarithm of weight $7-d$. Our approach is uniform with respect to $d$ and at the end relies on classical results about the action of Weyl groups on the set of lines contained in the considered del Pezzo surface. This series of `del Pezzo's hyperlogarithmic functional identities' is a natural generalization of the famous and well-know 3-term and 5-term identities of the logarithm and dilogarithm ('Abel's relation') which correspond to the cases when $d=6$ and $d=5$ respectively. This text ends with a section containing several questions and some possibly interesting perspectives.
