Timeline for Euler characteristic of cyclic quotients
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Jun 26, 2011 at 22:19 | comment | added | Cyrus | Dear Francesco. Thank you for your answer and also for introducing the paper. It was very helpful for me. | |
| Jun 26, 2011 at 16:25 | comment | added | Francesco Polizzi | In the case where $S$ is the minimal resolution of $T$, this is pretty classical stuff and it is related in some fascinating way to continuous fractions. You need of course to know how your group acts (there are several inequivalent actions of $\mathbb{Z}_n$ on $\mathbb{C}^2$). For a (by no means original) treatment, have a look at Sections $2$ and $3$ of my paper with E. Mistretta "Standard isotrivial fibrations with $p_g=q=1$ - II" (it is on the arXiv), in particular at Proposition 3.5. | |
| Jun 26, 2011 at 16:15 | comment | added | Torsten Ekedahl | Let $T$ be an abelian surface with $\{\pm1\}$ acting it. The quotient is a singular K3-surface and a resolution is a non-singular K3-surface. Both of them have Euler characteristic $2$ and $T$ has Euler characteristic $0$ so the answer to the last question is no. | |
| Jun 26, 2011 at 16:05 | comment | added | Cyrus | I mean the Euler characteristic of the structure sheaf as defined in Hartshorne p.230. | |
| Jun 26, 2011 at 15:58 | comment | added | Vivek Shende | what is the "sheaf theoretic Euler characteristic"? | |
| Jun 26, 2011 at 15:57 | history | edited | Cyrus | CC BY-SA 3.0 |
added 14 characters in body
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| Jun 26, 2011 at 15:45 | history | asked | Cyrus | CC BY-SA 3.0 |