Timeline for $Ext$-algebra of stable vector bundles
Current License: CC BY-SA 4.0
9 events
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| Jun 15, 2021 at 13:31 | history | edited | Libli | CC BY-SA 4.0 |
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| Jun 15, 2021 at 13:23 | history | edited | Libli | CC BY-SA 4.0 |
Some clarifications on the firts item of the answer.
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| Jun 15, 2021 at 13:20 | comment | added | Libli | @NicoBerger : you are right. I have had a wrong recollection of Suarez-Alvarez result. I used it some time ago to highlight some properties of Hochschild cohomology (where it applies, see section 2.5) and I wrongly remembered it was correct in a larger context. I will edit my answer. | |
| Jun 15, 2021 at 7:36 | comment | added | Nico Berger | I am sorry, I still have troubles understanding this in general. If we take in section 2.1 $\mathcal{C}=Coh(X)$, then the unit object is $\mathcal{O}_X$ and one concludes that $Ext^{\ast}(\mathcal{O}_X,\mathcal{O}_X)$ is graded-commutative. So this also holds for objects in the orbit of $\mathcal{O}_X$ under $Aut(\mathrm{D}^b(X))$. But for a general slope-stable vector bundle $E$ what is the category $\mathcal{C}$ to which we apply the discussion of section 2.1? | |
| Jun 14, 2021 at 20:20 | comment | added | Libli | @NicoBerger : you should have a look at section 2 of Suarez-Alvarez paper (and more precisely, section 2.1). | |
| Jun 14, 2021 at 12:31 | comment | added | Nico Berger | Thank you very much for this great answer! May I quickly ask how you apply the result of Suarez-Alvarez to obtain that $Ext^{\ast}(E,E)$ is graded-commutative, i.e. what is the suspended monoidal category such that the endomorphism ring of the unit object equals $Ext^{\ast}(E,E)$? | |
| Jun 14, 2021 at 9:45 | vote | accept | Nico Berger | ||
| Jun 12, 2021 at 13:11 | history | edited | Libli | CC BY-SA 4.0 |
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| Jun 12, 2021 at 9:46 | history | answered | Libli | CC BY-SA 4.0 |