Cuspidal plane curves, syzygies and a bound on the MW-rank

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• 作者：Remke Kloosterman¹ ; ^{klooster@math.hu-berlin.de}
• 关键词：14H30 ; 13D02 ; 14H50 ; 14J30
• 刊名：Journal of Algebra
• 出版年：2013
• 出版时间：1 February, 2013
• 年：2013
• 卷：375
• 期：Complete
• 页码：216-234
• 全文大小：266 K

文摘

Let be a reduced plane curve of degree 6k, with only nodes and ordinary cusps as singularities. Let I be the ideal of the points where C has a cusp. Let be a minimal resolution of I. We show that . From this we obtain that the Mordell-Weil rank of the elliptic threefold equals . Using this we find an upper bound for the Mordell-Weil rank of W, which is and we find an upper bound for the exponent of in the Alexander polynomial of C, which is . This improves a recent bound of Cogolludo and Libgober almost by a factor 2.