Timeline for Universal hyperplane section and nondegeneracy of general hyperplane section
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 27, 2023 at 14:51 | comment | added | Libli | @user7391733 : I am not sure the irreducibility assumption is helpful in any way. The result is still true when $X$ is reducible. This result is more of a cohomological nature than a topological one, so I guess one should not focus too much on the topological assumptions. | |
| Feb 27, 2023 at 12:36 | comment | added | user267839 | I understand, even if $X$ is NOT linear, there could occure troubles with the set $A:= \{(H, \Lambda) \ \vert H \cap X \subset \Lambda \}$. Actually I not pretty sure that it is aways closed in $ (\mathbb{P}^{n})^* \times \mathbb{G}(k,n)$ | |
| Feb 27, 2023 at 12:19 | comment | added | user267839 | you are right, the statement of exercise is wrong if $X$ has degree $1$ , ie is linear subspace. But if we add the assumpion that $X$ has degree $\ge2$, could we argue exploiting irreducibility of $\Omega_X$ as Harris suggested? | |
| Feb 27, 2023 at 11:58 | comment | added | Jason Starr | I am going to make a comment that perhaps I should keep to myself. I have taught out of that book, as well as other books (Mumford's "Red Book", Hartshorne's book, notes that Vakil, Buch, and I circulated for a while as postdocs). I think Harris's book is best viewed as a "problem book": the exercises are challenging and fun. Some of the actual proofs are spotty, to say the least. Personally, I would use Harris's book together with another textbook (which I would use for proofs). | |
| Feb 27, 2023 at 10:18 | history | edited | Libli | CC BY-SA 4.0 |
added 1 character in body
|
| Feb 27, 2023 at 10:03 | history | edited | Libli | CC BY-SA 4.0 |
added 1 character in body
|
| Feb 27, 2023 at 9:55 | history | edited | Libli | CC BY-SA 4.0 |
missing part of the answer
|
| Feb 27, 2023 at 9:40 | history | answered | Libli | CC BY-SA 4.0 |