Georgian Mathematical Journal 13 (2006), No. 3, 411--417
Copyright Heldermann Verlag 2006
Curves with Two Pencils and Associated Maps to Projective Spaces
Edoardo Ballico
Dept. of Mathematics, University of Trento, 38050 Povo, Italy
ballico@science.unitn.it
[Abstract-pdf]
Let $X$ be a smooth and connected projective curve. Assume the existence of spanned $L\in \mbox{Pic}^a(X)$, $R\in \mbox{Pic}^b(X)$ such that $h^0(X,L) = h^0(X,R)=2$ and the induced map $\phi _{L,R}:X \to {\bf {P}}^1\times {\bf {P}}^1$ is birational onto its image. Here we study the following question. What can be said about the morphisms $\beta :X \to {\bf {P}}^r$ induced by a complete linear system $\vert L^{\otimes u}\otimes R^{\otimes v}\vert$ for some positive $u, v$? We study the homogeneous ideal and the minimal free resolution of the curve $\beta (X)$.
Keywords: Maps to projective spaces, line bundles on curves, curves with two pencils, homogeneous ideal, minimal free resolution.
MSC: 14H51, 14H50
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