On higher syzygies of ruled surfaces |
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Authors: | Euisung Park |
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Affiliation: | School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongryangri 2-dong, Dongdaemun-gu, Seoul 130-722, Republic of Korea |
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Abstract: | We study higher syzygies of a ruled surface over a curve of genus with the numerical invariant . Let Pic be a line bundle in the numerical class of . We prove that for , satisfies property if and , and for , satisfies property if and . By using these facts, we obtain Mukai-type results. For ample line bundles , we show that satisfies property when and or when and . Therefore we prove Mukai's conjecture for ruled surface with . We also prove that when is an elliptic ruled surface with , satisfies property if and only if and . |
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Keywords: | |
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