A computational solution to a question by Reauville on the invariants of the binary quintic

JOURNAL OF ALGEBRA

卷:303

Article

Abdesselam, A.

关键词: invariant theory;    binary forms;    Tschirnhaus transformations;    del Pezzo surfaces;    pencils of quadrics;   

DOI  :  10.1016/j.jalgebra.2006.01.015

来源: Elsevier

【 摘 要 】

We obtain an alternative proof of an injectivity result by Beauville for a map from the moduli space of quartic del Pezzo surfaces to the set of conjugacy classes of certain subgroups of the Cremona group. This amounts to showing that a projective configuration of five distinct unordered points on the line can be reconstructed from its five projective four-point subconfigurations. This is done by reduction to a question in the classical invariant theory of the binary quintic, which is solved by computer-assisted methods. More precisely, we show that six specific invariants of degree 24, the construction of which was explained to us by Beauville, generate all invariants whose degree is divisible by 48. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free