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Jun 21, 2017 at 16:03 comment added pw1 Thank you! It seemed like it should be something simple, but I just wasn't seeing it!
Jun 21, 2017 at 15:47 comment added Xarles At the level of points: any point of $Proj(V)$ is given by a vector $v$ non zero in $V$ modulo homothety. It has a representative in $M$ whose image in $k\otimes M$ is non-zero. This imatge, modulo homothety in $k$, is the image of the reduction map.
Jun 21, 2017 at 15:06 history edited YCor
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Jun 21, 2017 at 14:45 history asked pw1 CC BY-SA 3.0