Timeline for When is bijective map between closed point of varieties a morphism?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 22, 2022 at 22:55 | comment | added | Will Sawin | @LSpice Yes, but existence is a consequence of the existence of $P$, not of the existence of $f$. | |
| Apr 22, 2022 at 22:05 | comment | added | LSpice | Sure, uniqueness is surely implicit, but isn't the quoted passage also claiming existence? | |
| Apr 22, 2022 at 22:00 | comment | added | Will Sawin | @LSpice To me the phrase "induces a morphism" implies uniqueness. But my goal was also to answer the question about "I meet in some papers in complex algebraic geometry that people define a morphism by claiming on closed points." You can't define a morphism in this way unless you specify a unique morphism. | |
| Apr 22, 2022 at 21:49 | comment | added | LSpice | But the quoted passage is really saying that a bijection comes from a morphism, not just that, if it comes from a morphism, then it comes from a unique such … isn't it? | |
| Apr 22, 2022 at 21:09 | history | answered | Will Sawin | CC BY-SA 4.0 |