1
$\begingroup$

Let $H = Hilb_{d,g,r}$ be the Hilbert scheme of genus $g$ curves of degree $d$ in proyective space $\mathbb{P}^r$, over an algebraically closed field $k$.

Is it true that the set of points of $H$ consisting of smooth curves is open in $H$? If so, how do I see this?

Edit: added the hypothesis that the base field is algebraically closed.

Improve this question
$\endgroup$
1
  • 2
    $\begingroup$ Please look up `generic smoothness' and see how it can be applied. $\endgroup$
    – Mohan
    Commented Jul 28, 2015 at 23:36

0

Reset to default

You must log in to answer this question.