Journal of the Mathematical Society of Japan

Variety of nets of degree g-1 on smooth curves of low genus

Kyung-Hye CHO, Changho KEEM, and Akira OHBUCHI

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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.

Article information

Source
J. Math. Soc. Japan, Volume 55, Number 3 (2003), 591-616.

Dates
First available in Project Euclid: 3 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191418991

Digital Object Identifier
doi:10.2969/jmsj/1191418991

Mathematical Reviews number (MathSciNet)
MR1978211

Zentralblatt MATH identifier
1033.14015

Subjects
Primary: 14H45: Special curves and curves of low genus 14H10: Families, moduli (algebraic) 14C20: Divisors, linear systems, invertible sheaves

Keywords
algebraic curves linear series branched covering

Citation

CHO, Kyung-Hye; KEEM, Changho; OHBUCHI, Akira. Variety of nets of degree $g-1$ on smooth curves of low genus. J. Math. Soc. Japan 55 (2003), no. 3, 591--616. doi:10.2969/jmsj/1191418991. https://projecteuclid.org/euclid.jmsj/1191418991


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