Rational curves of degree 16 on a general heptic fourfold

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• 作者：Ethan Cotterill
• 关键词：13P10 ; 14H45
• 刊名：Journal of Pure and Applied Algebra
• 出版年：January, 2014
• 年：2014
• 卷：218
• 期：1
• 页码：121-129
• 全文大小：377 K

文摘

According to a conjecture of H. Clemens, the dimension of the space of rational curves on a general projective hypersurface should equal the number predicted by a na茂ve dimension count. In the case of a general hypersurface of degree 7 in , the conjecture predicts that the only rational curves should be lines. This has been verified by Hana and Johnsen for rational curves of degree at most 15. Here we extend their results to show that no rational curves of degree 16 lie on a general heptic fourfold.