Curves with Two Pencils and Associated Maps to Projective Spaces
Keyword(s):
Abstract Let 𝑋 be a smooth and connected projective curve. Assume the existence of spanned 𝐿 ∈ Pic𝑎(𝑋), 𝑅 ∈ Pic𝑏(𝑋) such that ℎ0(𝑋, 𝐿) = ℎ0(𝑋, 𝑅) = 2 and the induced map ϕ 𝐿,𝑅 : 𝑋 → 𝐏1 × 𝐏1 is birational onto its image. Here we study the following question. What can be said about the morphisms β : 𝑋 → 𝐏𝑅 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).
1980 ◽
Vol 4
(2)
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pp. 269-279
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2009 ◽
Vol 213
(3)
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pp. 360-369
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2004 ◽
Vol 56
(4)
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pp. 716-741
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1990 ◽
Vol 49
(3)
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pp. 364-385
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1990 ◽
Vol 118
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pp. 203-216
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2010 ◽
Vol 214
(6)
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pp. 850-861
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1995 ◽
Vol 168
(1)
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pp. 63-74
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2007 ◽
Vol 311
(2)
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pp. 435-462
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