I'm sure this question has been asked before...
Till today, I thought that one cannot define a global holomorphic vector field on a two-sphere due to the hairy ball theorem. However, here's an exercise which I found on page 8 of the "Mirror symmetry" book (see pic attached):
Could anyone comment on this please? Doesn't defining a global holomorphic vector field on a sphere imply defining a global section on the tangent vector bundle? I am confused.
Thanks.