Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 55, Number 3 (2003), 591-616.
Variety of nets of degree on smooth curves of low genus
We classify smooth complex projective algebraic curves of low genus such that the variety of nets has dimension . We show that is equivalent to the following conditions according to the values of the genus . is either trigonal, a double covering of a curve of genus 2 or a smooth plane curve degree 6 for . is either trigonal, a double covering of a curve of genus 2, a tetragonal curve with a smooth model of degree 8 in or a tetragonal curve with a plane model of degree 6 for . is either trigonal or has a birationally very ample for or .
J. Math. Soc. Japan, Volume 55, Number 3 (2003), 591-616.
First available in Project Euclid: 3 October 2007
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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