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Timeline for When is a blow-up non-singular?

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Jul 12, 2021 at 19:00 comment added Student85 Sorry, this question is amazing for me. In the case when $Bl_{Z}(X)$ is non singular, what can happen with $E= \pi^{-1}(Z)$? This is a divisor contained in $Bl_{Z}(X)$. This is smooth (non singular) or singular? When it is singular, what type of singularities (dimension) ?
Mar 14, 2019 at 1:25 comment added sdey Sorry for commenting on such an old question ... the current answers are already amazing, but apart from that I couldn't resist myself from mentioning one relevant paper : On the smoothness of blowups for certain monomial curves, Mukhopadhyay, D. & Sengupta, I. Beitr Algebra Geom (2012) 53: 89. link.springer.com/article/10.1007/s13366-011-0068-0
Apr 13, 2017 at 12:58 history edited CommunityBot
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S Nov 3, 2010 at 5:31 vote accept jlk
S Nov 3, 2010 at 5:31 vote accept jlk
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