Double coverings of hyperelliptic real algebraic curves

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• 作者：E. Bujalance ; F.J. Cirre ; J.M. Gamboa
• 关键词：Phloem ; Signalling ; Intercellular transport ; Plasmodesmata ; Sugars ; Macromolecules ; RNA
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2008
• 出版时间：September 2008
• 年：2008
• 卷：212
• 期：9
• 页码：2011-2026
• 全文大小：367 K

文摘

We consider double and (possibly) branched coverings f=""/science?_ob=MathURL&_method=retrieve&_udi=B6V0K-4S035HS-3&_mathId=mml56&_user=1067359&_cdi=5649&_rdoc=2&_acct=C000050221&_version=1&_userid=10&md5=4b7524b90c740dcd76ceaa5babe72fe0"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">π:X→X^′ between real algebraic curves where f=""/science?_ob=MathURL&_method=retrieve&_udi=B6V0K-4S035HS-3&_mathId=mml57&_user=1067359&_cdi=5649&_rdoc=2&_acct=C000050221&_version=1&_userid=10&md5=a62a4b6155f7423de60d94cae3a2a922"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">X is hyperelliptic. We are interested in the topology of such coverings and also in describing them in terms of algebraic equations. In this article we completely solve these two problems. We first analyse the topological features and ramification data of such coverings. Second, for each isomorphism class of these coverings we then describe a representative, with defining polynomial equations for f=""/science?_ob=MathURL&_method=retrieve&_udi=B6V0K-4S035HS-3&_mathId=mml58&_user=1067359&_cdi=5649&_rdoc=2&_acct=C000050221&_version=1&_userid=10&md5=ab02258b775d68477902b8be18f204a2"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">X and for f=""/science?_ob=MathURL&_method=retrieve&_udi=B6V0K-4S035HS-3&_mathId=mml59&_user=1067359&_cdi=5649&_rdoc=2&_acct=C000050221&_version=1&_userid=10&md5=a6e09052fe098f5e081e60391c0872f3"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">X^′, a formula for the involution that generates the covering transformation group, and a rational formula for the covering projection f=""/science?_ob=MathURL&_method=retrieve&_udi=B6V0K-4S035HS-3&_mathId=mml60&_user=1067359&_cdi=5649&_rdoc=2&_acct=C000050221&_version=1&_userid=10&md5=6d6915349617cfb30b3cacbec6248d12"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">π:X→X^′.