Op 22-05-2012 15:26, Volker Braun schreef: > On Tuesday, May 22, 2012 4:16:08 AM UTC-4, Marco Streng wrote: > > Definitely! That would make it possible to have a smooth projective > model, with the correct points at infinity. > > > I don't understand that sentence - a smooth elliptic surface can already > be embedded in P^2, right?
That sentence refers to the sentence by David Eklund right above it. So it has nothing to do with elliptic surfaces, but is about hyperelliptic curves. Hyperelliptic curves can be mapped birationally onto a curve in P^2, just by going via the standard model in A^2 of the form y^2 + h(x)*y = f(x). But the image is not smooth at infinity for any hyperelliptic curve (of genus >=2). To make the image smooth, the standard solutions are to 1) glue two copies of A^2, 2) use a higherdimensional P^n, or 3) use a weighted projective 2-dimensional space. I think David was aiming at (3), and I was simply welcoming that. > > Note that the toric variety code assumes that the base ring is a field > at various places. So for number theory purposes it might be good to > split things into ToricVariety_ring vs. ToricVariety_field. Its mostly > my ignorance about toric varieties over general rings that prevented me > from doing so... > > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
