Stability of pencils of plane sextics and Halphen pencils of index two

Author:

Zanardini AlineORCID

Abstract

AbstractWe study the problem of classifying pencils of plane sextics up to projective equivalence via geometric invariant theory (GIT). In particular, we provide a complete description of the GIT stability of certain pencils of plane sextics called Halphen pencils of index two-classical geometric objects which were first introduced by G. Halphen in 1882. Inspired by the work of Miranda on pencils of plane cubics, we obtain explicit stability criteria in terms of the types of singular fibers appearing in their associated rational elliptic surfaces.

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Explicit constructions of Halphen pencils of index two;Rocky Mountain Journal of Mathematics;2022-08-01

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