Timeline for Extend algebraic morphism to a compactification with normal crossing boundary
Current License: CC BY-SA 4.0
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| Nov 27 at 12:38 | comment | added | R. van Dobben de Bruyn | To be fair, most working algebraic geometers' knowledge of resolution of singularities consists of knowing the statements (and the proof in dimension $2$). You can deduce a positive answer to your question easily from Hironaka (plus Nagata compactification). Choose compactifications $\bar X$ and $\bar Y$ of $X$ and $Y$ respectively. Blowing up in $\bar Y \setminus Y$, you can make $\bar Y$ smooth with normal crossings boundary. Replace $\bar X$ by the closure of the graph of $f \colon X \to \bar Y$ in $\bar X \times \bar Y$ to assume $f$ extends, and then apply resolution to $\bar X$. | |
| Nov 27 at 7:50 | history | asked | Richard | CC BY-SA 4.0 |