# Is there a way to make MAGMA work with surfaces over weighted projective spaces?

Is there a way to use MAGMA to study surfaces defined over a weighted projective space (by "study" I mean computing e.g. invariants (e.g. $p_a$, $p_g$), singularities, etc)? For example, I was trying, as a trial test, to get MAGMA working on Chatelet surfaces with affine equation $y^2 - az^2 = P(x)$, but with no success. Any idea?

• I don't think that Châtelet surfaces natually embed into a weighted projective space (if you try it you will get some singularities). Being a conic bundle over $\mathbb{P}^{1}$, they rather naturally embed into some $\mathbb{P}^2$-bundle over $\mathbb{P}^1$. – Daniel Loughran Feb 20 '14 at 21:15