I am reading some notes about elliptic curves right now and the author mentions the alternative Jacobian projective coordinates, where one establishes the equivalence $(x,y,z)\sim (\lambda^2 x, \lambda^3 y, \lambda z)$ so that the homogeneous general equation of the elliptic curve is $y^2=x^3+Axz^4+Bz^6$. The author then states that the point at infinity is $[0:1:0]$ just as in usual coordinates.
This is a mistake, right? The point $[0:1:0]$ is not on that curve; the point at infinity should be $[1:1:0]$, no?
You are correct that $[0:1:0]$ is not on the curve $y^2=x^3+Axz^4+Bz^6$ in those modified projective coordinates $[x:y:z]$, and $[1:1:0]$ is indeed on the curve. I am not an expert though in cryptography... the literature in cryptography seems to insist in calling the point at infinity by $[0:1:0]$ even though this point is not on the curve in those coordinates (see this book for example). So it might be the case that calling the point at infinity $[0:1:0]$ is just a label (referring to the usual projective coordinates) and not meaning to imply that $x=0$, $y=1$, $z=0$ satisfy the modified equation. It seems, however, that some books do not follow this confusing 'convention' if that's really the case.