Timeline for Can any radiciel morphism be presented as the composition of a universal homeomorphism with an immersion?
Current License: CC BY-SA 2.5
6 events
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| Mar 22, 2011 at 20:03 | comment | added | Laurent Moret-Bailly | Well, take $Y$ to be an irreducible curve with one node, and $X=$ the normalization minus one of the points above the node. | |
| Mar 22, 2011 at 19:15 | comment | added | Mikhail Bondarko | Thank you! Actually, I am mostly interested in the case when $X$ is regular and connnected (see the update). Does this help? | |
| Mar 22, 2011 at 19:10 | history | edited | Mikhail Bondarko | CC BY-SA 2.5 |
added 157 characters in body
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| Mar 22, 2011 at 16:24 | comment | added | Angelo | I just saw Laurent's comment. Since he makes exactly the same points as my answer, and was posted earlier, I deleted my answer. | |
| Mar 22, 2011 at 15:51 | comment | added | Laurent Moret-Bailly | There are lots of monomorphisms of schemes (even of finite type) which are not of this form: take $Y=\mathbb{A}^1_k$ ($k$ a field) and take for $X$ the disjoint union of $\mathbb{G}_{m,k}$ and the origin. You need to assume, at least, that $f$ is a homeomorphism on its image, plus something to ensure that the image is locally closed (think of the inclusion of a generic point). | |
| Mar 22, 2011 at 11:53 | history | asked | Mikhail Bondarko | CC BY-SA 2.5 |