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Curves with Two Pencils and Associated Maps to Projective Spaces

Curves with Two Pencils and Associated Maps to Projective Spaces 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). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Curves with Two Pencils and Associated Maps to Projective Spaces

Georgian Mathematical Journal , Volume 13 (3) – Sep 1, 2006

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References (12)

Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2006.411
Publisher site
See Article on Publisher Site

Abstract

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).

Journal

Georgian Mathematical Journalde 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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