If we let $M$ be a quasi-affine variety, is it true in general that the blowup of $M$ at a non-singular point $p$ does not introduce new singularities? I came across this statement in my reading, but I'm not actually convinced that this is true. Am I missing a simple argument?
2026-03-26 03:01:39.1774494099
Is it true that blowing up a quasi-affine variety at a nonsingular point never introduces new singularities?
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