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May 11, 2010 at 5:11 vote accept Chirag Lakhani
May 9, 2010 at 20:31 vote accept Chirag Lakhani
May 11, 2010 at 5:10
May 7, 2010 at 10:59 comment added quim As implied by Torsten's answer, one can get information from $g_{s+1}$ only together with $g_s$. The common locus of $g_s$ and $g_{s+1}$ mentioned in the question is an example. If you blow up the origin, and p is a point of the strict transform X on the exceptional divisor, then one can read smoothness of X at p (and the tangent hyperplane $T_p X$) from $g_s$ and $g_{s+1}$ together. Under some genericity conditions one should be able to read the tangent cones also, I guess.
May 7, 2010 at 4:11 history answered Torsten Ekedahl CC BY-SA 2.5