Original sentence: There is a converse, which is a corollary to the Riemann-Roch theorem: a non-singular curve C of genus g embedded in projective space of dimension g − 1 as a curve of degree 2g − 2 is a canonical curve, provided its linear span is the whole space
Edited sentence: There is a converse, which is a corollary to the Riemann-Roch theorem: a non-singular curve C of genus g embedded in projective space of dimension g − 1 as a linearly normal curve of degree 2g − 2 is a canonical curve, provided its linear span is the whole space