Timeline for Factoriality of cones

7 events

when toggle format	what		by	license	comment
Dec 17, 2012 at 15:09	vote	accept	gio
Dec 17, 2012 at 15:00	comment	added	Francesco Polizzi		Of course you can consider cones with positive dimensional vertex, but I do not know if there is an analog of Lipman's results for them. So I restricted myself to the case where the vertex is a point.
Dec 17, 2012 at 14:56	comment	added	Francesco Polizzi		If $X$ is a Grassmannian, then $X$ is smooth. It is not difficult to see that the image of $X$ under the Plucker embedding is projectively normal and that $\textrm{Pic}(X)=\mathbb{Z}$, see mathoverflow.net/questions/7604/…. So any divisor on $X$ is an integer multiple of the hyperplane section, in other words for Grassmannians (1) is satisfied.
Dec 17, 2012 at 14:44	comment	added	gio		My real question is when your condition (1c) is also satisfied. But why do you request that the vertex of the cone is a point? Moreover, can I have some elucidation/reference on the fact that (1c) implies (1) ?
Dec 17, 2012 at 14:34	history	edited	Francesco Polizzi	CC BY-SA 3.0	deleted 8 characters in body
Dec 17, 2012 at 14:26	history	edited	Francesco Polizzi	CC BY-SA 3.0	added 512 characters in body; deleted 163 characters in body; deleted 3 characters in body
Dec 17, 2012 at 14:17	history	answered	Francesco Polizzi	CC BY-SA 3.0