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Mar 23, 2016 at 13:49 comment added abx Why do you need Fulton's construction? Your equality only involves tangent bundles of smooth varieties. $\tilde{X} $ is a hypersurface in $B_p(\Bbb{P^n})$, where $p$ is the singular point of $X$. The formula for $[T_{\tilde{X} }]$ follows immediately from the normal bundle exact sequence for $\tilde{X}\subset B_p(\Bbb{P^n})$.
Mar 23, 2016 at 11:02 history asked user3001 CC BY-SA 3.0