Abstract:In the present paper we compute Alexander polynomials for certain classes of conic-line arrangements in the complex projective plane which are related to pencils. We prove two general results for curve arrangements coming from Halphen pencils of index $k\geq 2$. Then we apply them to the Hesse arrangement of conics and to some of its degenerations. The results are completed by computations using computer algebra. In particular, we construct conic-line arrangements which are non-reduced pencil-type arrangements and have as roots of their Alexander polynomials roots of unity of order 7. Such roots are not known and are conjectured not to exist in the class of line arrangements.
From: Piotr Pokora [view email]
[v1]
Tue, 2 May 2023 14:29:14 UTC (16 KB)
[v2]
Mon, 22 May 2023 12:08:05 UTC (21 KB)
[v3]
Fri, 17 Oct 2025 17:48:34 UTC (23 KB)
[v4]
Mon, 14 Sep 2026 08:49:45 UTC (23 KB)
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