Abstract
In this paper, we present a duality construction for multiarcs in projective Hjelmslev geometries over chain rings of nilpotency index 2. We compute the parameters of the resulting arcs and discuss some examples.
Highlights
Êo ÊÓÑÔÓÒ ÒØÛ × ̧ ÑÙÐØ ÔÐ Ø ÓÒ (x0 + x1t)(y0 + y1t) = x0y0 + (x0y1 + x1σ(y0))t Rσ = Fq[t; σ]/(t2)o.
ÐÓ × Ö Ò GR(q2, p2) = Zp2[X]/ (f (X)) ̧ f (X) × ÑÓÒ Ó Ö r p × ÖÖ Ù Ð ÖÖ Ù Ð ÑÓ μo.
⌢⌣ 1 Ò ÓÙÖ Ö Ð Ø ÓÒÆ1⁄2μ X ⌢⌣ Y ∃s, t ∈ L : X, Y Is, X, Y ItÆ3⁄4μ s ⌢⌣ t ∃X, Y ∈ P : X, Y Is, X, Y Ito
Summary
ÓÑÔÓÒ ÒØÛ × ̧ ÑÙÐØ ÔÐ Ø ÓÒ (x0 + x1t)(y0 + y1t) = x0y0 + (x0y1 + x1σ(y0))t Rσ = Fq[t; σ]/(t2)o. ÐÓ × Ö Ò GR(q2, p2) = Zp2[X]/ (f (X)) ̧ f (X) × ÑÓÒ Ó Ö r p × ÖÖ Ù Ð ÖÖ Ù Ð ÑÓ μo. ⌢⌣ 1 Ò ÓÙÖ Ö Ð Ø ÓÒÆ1⁄2μ X ⌢⌣ Y ∃s, t ∈ L : X, Y Is, X, Y ItÆ3⁄4μ s ⌢⌣ t ∃X, Y ∈ P : X, Y Is, X, Y Ito
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