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 .
"Variety of nets of degree on smooth curves of low genus." J. Math. Soc. Japan 55 (3) 591 - 616, July, 2003. https://doi.org/10.2969/jmsj/1191418991