The space of lines in cyclic covers of projective space期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The space of lines in cyclic covers of projective space

Institution:	1. Korea Institute for Advanced Study, Hoegiro 87, Seoul 130-722, Republic of Korea;2. Department of Mathematics, University of California, Riverside CA 92521, United States of America;1. The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India;2. Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA;1. Department of Mathematics, Illinois State University, Normal, IL 61790, USA;2. Department of Mathematics, Gettysburg College, Gettysburg, PA 17325, USA;1. Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea;2. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Republic of Korea

Abstract:	Take positive integers m, n and d. Let Y be an m-fold cyclic cover of $P^{n}$ ramified over a general hypersurface $X ? P^{n}$ of degree md. In this paper we study the space $F (Y)$ of lines in Y and show that it is smooth of dimension $2 (n ? 1) ? d (m ? 1)$ if $m d > 2 n ? 3$ and $2 (n ? 1) ? d (m ? 1) \geq 0$ . When $2 (n ? 1) = d (m ? 1)$ , our result gives a formula on the number of m-contact order lines of X (see Definition 1.2).

Keywords:	Cyclic cover Fano scheme Bitangents
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