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Dec 29, 2012 at 18:38 comment added Jérémy Blanc Why do you want to use Macaulay2 ? It is smooth by the argument of Piotr (replacing $t^2$ by $t$ to get really a map from $P^1$ to $P^9$). If you want to do it in coordinates, look at the set where t=1 and the set where s=1. This seems to be a trivial exercise, not really for MO.
Dec 29, 2012 at 15:21 comment added Mahdi Majidi-Zolbanin Use Macaulay2 for this type of calculations. It can tell you the codimension of the singular locus.
Dec 29, 2012 at 9:24 comment added Piotr Achinger If we replace $t^2$ by $t$, the map $\phi$ becomes the $9$-uple embedding of $\mathbb{P}^1$. In particular, it is a closed immersion and the image is smooth.
Dec 29, 2012 at 9:02 answer added Serge Lvovski timeline score: 1
Dec 29, 2012 at 8:43 history asked Stiger CC BY-SA 3.0