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F. Severi
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Ulrich Frank, H. Adelsberger, Peter Chamoni, Frank-Dieter Dorloff, K. Echtle, Stefan Eicker, Michael Goedicke, Tobias Kollmann, Bruno Müller-Clostermann, Klaus Pohl, Erwin Rathgeb, Rainer Unland, S. Zelewski, Peter Berger, T. Luckmann, F. Nietzsche (2005)
Author’s Address:
Let 𝑋 be a smooth and connected projective curve. Assume the existence of spanned 𝐿 ∈ Pic 𝑎 (𝑋), 𝑅 ∈ Pic 𝑏 (𝑋) such that ℎ 0 (𝑋, 𝐿) = ℎ 0 (𝑋, 𝑅) = 2 and the induced map φ 𝐿,𝑅 : 𝑋 → 𝐏 1 × 𝐏 1 is birational onto its image. Here we study the following question. What can be said about the morphisms β : 𝑋 → 𝐏 𝑅 induced by a complete linear system |𝐿 ⊗𝑢 ⊗𝑅 ⊗𝑣 | for some positive 𝑢, 𝑣? We study the homogeneous ideal and the minimal free resolution of the curve β (𝑋).
Georgian Mathematical Journal – de Gruyter
Published: Sep 1, 2006
Keywords: Maps to projective spaces; line bundles on curves; curves with two pencils; homogeneous ideal; minimal free resolution
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