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Curves without plane model of small degree

✍ Scribed by Changho Keem; Gerriet Martens

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
141 KB
Volume
281
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let C be a smooth irreducible projective curve of genus g > 0 and s~C~ (2) the minimal degree of plane models of C. Clearly, s~C~ (2) ≀ g + 2. Our main result is: s~C~ (2) = g + 2 – t (for some integer t β‰₯ 0) implies that C is a double cover of a curve of genus at most t provided that g is not too small with respect to t. For small t we can be more precise. (Β© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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