Timeline for How to calculate : $ \mathrm{Hdg}^{ 2 \bullet } ( \mathcal{H}\mathrm{ilb} ( \mathbb{P}^n ),\mathbb{Q} ) $?
Current License: CC BY-SA 4.0
11 events
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| Aug 23, 2018 at 10:44 | comment | added | YoYo | Thank you very much @Jason Starr. I will see in this direction. Thank you. :-D | |
| Aug 23, 2018 at 10:22 | comment | added | Jason Starr | I thought, at first, you were asking for $n=2$, computed by Ellingsrud and Stromme in "On the homology of the Hilbert scheme of points in the plane", Invent. Math. 87 (1987), 343-352 To the best of my knowledge, the Hodge-Deligne polynomials are unknown for arbitrary $n$, in part because the Hilbert schemes are singular for $n>2$. However, there is still a Bialynicki-Birula stratification of the Hilbert scheme in the singular case, and I believe that the Hilbert scheme is still cellular (so HD polys are "diagonal"). Please confer papers of Gusein-Zade, Luengo, and Melle-Hernandez. | |
| Aug 23, 2018 at 10:01 | comment | added | YoYo | Yes, It's just a name of a famous artist. It's not important. :-) Please, give me some help. I need it. :-) | |
| Aug 23, 2018 at 9:56 | comment | added | Jason Starr | Did the username of the OP just change? | |
| Aug 23, 2018 at 9:45 | comment | added | YoYo | I can't follow you in these explanations since I do not have yet the level for that, nevertheless, can you tell me which are the books that treat of these subjects there : the (k,k)-components of the associated graded pure Hodge structures of the weight filtration, "diagonal" coefficients of the Hodge-Deligne polynomial. @Jason Starr : Can you please tell me where exactly can i find about the algebraic cell decomposition of $ \mathcal{H} \mathrm{ilb} ( \mathbb{P}^n ) $ in the work of Ellingsrud and Stromme ?. In which book ? What is its title please ? Thank you very much. | |
| Aug 23, 2018 at 9:19 | comment | added | Jason Starr | @abx. Perhaps the OP just wanted the direct sum of the $(k,k)$-components of the associated graded pure Hodge structures of the weight filtration ("diagonal" coefficients of the Hodge-Deligne polynomial). | |
| Aug 23, 2018 at 7:54 | comment | added | abx | Are you aware that $\mathcal{H}\mathrm{ilb}(\mathbb{P}^n)$ is highly singular for $n\geq 3$? Given that, what is $H^{k,k}(\mathcal{H}\mathrm{ilb}(\mathbb{P}^n))$? | |
| Aug 23, 2018 at 2:42 | comment | added | YoYo | Thank you very much @Jason Starr for your answer. :-) Can you give me please, some titles of books or articles of Ellingsrud and Stromme where i can find about the algebraic cell decomposition of $ \mathcal{H} \mathrm{ilb} ( \mathbb{P}^n ) $ that you told me in your comment above ? Thank you. :-) | |
| Aug 23, 2018 at 1:17 | comment | added | Jason Starr | There is an algebraic cell decomposition of the Hilbert schemes of finite length closed subschemes of $\mathbb{P}^n$, cf. the work of Ellingsrud and Stromme. Thus, all of the rational cohomology is Tate type. | |
| Aug 22, 2018 at 19:34 | history | edited | YoYo | CC BY-SA 4.0 |
added 16 characters in body
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| Aug 22, 2018 at 19:21 | history | asked | YoYo | CC BY-SA 4.0 |