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July, 2003 Variety of nets of degree g-1 on smooth curves of low genus
Kyung-Hye CHO, Changho KEEM, Akira OHBUCHI
J. Math. Soc. Japan 55(3): 591-616 (July, 2003). DOI: 10.2969/jmsj/1191418991

Abstract

We classify smooth complex projective algebraic curves C of low genus 7g10 such that the variety of nets Wg-12(C) has dimension g-7. We show that dimWg-12(C)=g-7 is equivalent to the following conditions according to the values of the genus g. (i)C is either trigonal, a double covering of a curve of genus 2 or a smooth plane curve degree 6 for g=10. (ii)C is either trigonal, a double covering of a curve of genus 2, a tetragonal curve with a smooth model of degree 8 in P3 or a tetragonal curve with a plane model of degree 6 for g=9. (iii)C is either trigonal or has a birationally very ample g62 for g=8 or g=7.

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Kyung-Hye CHO. Changho KEEM. Akira OHBUCHI. "Variety of nets of degree g-1 on smooth curves of low genus." J. Math. Soc. Japan 55 (3) 591 - 616, July, 2003. https://doi.org/10.2969/jmsj/1191418991

Information

Published: July, 2003
First available in Project Euclid: 3 October 2007

zbMATH: 1033.14015
MathSciNet: MR1978211
Digital Object Identifier: 10.2969/jmsj/1191418991

Subjects:
Primary: 14C20 , 14H10 , 14H45

Keywords: algebraic curves , branched covering , linear series

Rights: Copyright © 2003 Mathematical Society of Japan

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Vol.55 • No. 3 • July, 2003
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