Timeline for Connected components of a codimension one fiber for a finite morphism
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 27, 2020 at 17:36 | comment | added | Sasha | If $f$ is a morphism of curves, there is no better bound than the degree of the morphism. | |
| Feb 27, 2020 at 16:19 | comment | added | Flyingpanda | Yes, this is a good example. | |
| Feb 27, 2020 at 16:18 | comment | added | Bort | No, the number of connected components does not equal the number of irreducible components. For example take $X \rightarrow \mathbf P^2$ a double cover branched over a smooth quartic curve $C$. For a line $L \subset \mathbf P^2$ that is bitangent to $C$ the inverse image of $L$ is a union of 2 intersecting copies of $\mathbf P^1$. | |
| Feb 27, 2020 at 15:56 | history | edited | Flyingpanda | CC BY-SA 4.0 |
added 98 characters in body
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| Feb 27, 2020 at 15:53 | comment | added | Flyingpanda | But this is not sufficient... I expect this to be the number of $D_i$ or at least related to that... | |
| Feb 27, 2020 at 15:49 | comment | added | Sasha | It is bounded by the degree of the morphism. | |
| Feb 27, 2020 at 15:42 | history | asked | Flyingpanda | CC BY-SA 4.0 |