Pencils on real curves. Issue 8 (7th January 2013)

• Record Type: Journal Article
• Authors: Coppens, Marc; Huisman, Johannes
• Is Part Of: Mathematische Nachrichten. Volume 286:Issue 8/9(2013)
• Page Start: 799
• Page End: 816
• Publication Date: 2013-01-07
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201100196
• Languages: English
• ISSNs: 0025-584X

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>We consider coverings of real algebraic curves to real rational algebraic curves. We show the existence of such coverings having prescribed topological degree on the real locus. From those existence results we prove some results on Brill‐Noether Theory for pencils on real curves. For coverings having topological degree <tex-math notation="LaTeX"><![CDATA[\documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\underline{0}$\end{document}]]></tex-math><inline-graphic xlink:href="ark:/27927/pgg21cvxv2w" mimetype="image" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /> we introduce the covering number <italic>k</italic> and we prove the existence of coverings of degree 4 with prescribed covering number.</p> </abstract>