Timeline for topological Euler characteristic of canonical divisor
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 17, 2022 at 9:04 | vote | accept | user283487 | ||
| Nov 17, 2022 at 7:29 | comment | added | Francesco Polizzi | In fact, this approach only works in the case where the variety that we blow-up has trivial canonical class. So, for instance, we might look for a Calabi-Yau threefold $Y$ with $\chi_{\operatorname{top}}(Y)=-2$ and blow-up it at a point (this is the strategy of Sasha's answer). | |
| Nov 17, 2022 at 7:22 | comment | added | Francesco Polizzi | @abx: you are clearly right. I realized this as soon as I took paper and pencil :) | |
| Nov 17, 2022 at 7:13 | answer | added | Sasha | timeline score: 4 | |
| Nov 17, 2022 at 4:26 | comment | added | abx | @Francesco Polizzi: it doesn't exist. The canonical system of the blown-up variety has a fixed part, namely the 4 exceptional divisors. | |
| Nov 16, 2022 at 22:16 | comment | added | Francesco Polizzi | @JasonStarr: Actually, I do not know whether it exists. It is part of my "What happens..." | |
| Nov 16, 2022 at 21:33 | comment | added | Jason Starr | @FrancescoPolizzi. Why is there a smooth irreducible divisor in the canonical linear system of that blowing up? | |
| Nov 16, 2022 at 18:25 | comment | added | user283487 | @FrancescoPolizzi Thank you for your example! | |
| Nov 16, 2022 at 17:47 | comment | added | Francesco Polizzi | What happens if you consider the blow-up at 4 points of the product $C \times C \times C$, where $C$ is a smooth curve of genus $2$? | |
| S Nov 16, 2022 at 14:20 | review | First questions | |||
| Nov 16, 2022 at 14:32 | |||||
| S Nov 16, 2022 at 14:20 | history | asked | user283487 | CC BY-SA 4.0 |