Suppose you have a curve C such that degKC=0 and Gamma(C,Omega1C)neq0. Does this automatically imply that varthetaCequivOmega1C? My thought is yes, I've seen a proposition (Stanford AG course notes) that varthetaCequivOmega1C for a nonsingular plane cubic, but the proof is done in a particular case, and I must think there is easier way to show this. In particular, what is the morphism?
Thank you, just trying to make sense of this concept.
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