Timeline for Properties of a particular Kummer Surface
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 31, 2019 at 3:18 | comment | added | Soby | @Mark Alright I will take a look at those papers. Thank you very much! | |
| Jan 30, 2019 at 16:57 | comment | added | user47305 | Check out Catanase-Oguiso-Truong, "Unirationality of Ueno-Campana’s threefold", where they prove the three-dimensional one is unirational. You might also like Oguiso & Truong, "Explicit Examples of rational and Calabi-Yau threefolds with primitive automorphisms of positive entropy", which proves the three-dimensional one is rational if you use the curve with an order 6 auto instead. For the 2-diml one I don't know a reference offhand, but I bet you can figure it out from these other papers. | |
| Jan 30, 2019 at 16:50 | comment | added | Soby | @Mark Are there any papers giving a detailed study of this particular construction? I can't seem to find any. I can only find papers detailing constructions where they consider the quotient by an involution. | |
| Jan 30, 2019 at 15:36 | comment | added | user47305 | The fact that it's rational needs a justification too (probably Castelnuovo's criterion). One can do the same contruction in any dimension $n$ (take the quotient of $\mathbb C/\mathbb Z[i])^n$ by the diagonal action of $i$) and I believe it's unknown for what values of $n$ the quotient is a rational variety. | |
| Jan 30, 2019 at 6:35 | review | Close votes | |||
| Feb 8, 2019 at 20:55 | |||||
| Jan 30, 2019 at 6:32 | history | undeleted | Soby | ||
| Jan 29, 2019 at 11:55 | history | deleted | Soby | via Vote | |
| Jan 29, 2019 at 11:25 | review | Close votes | |||
| Jan 29, 2019 at 12:00 | |||||
| Jan 29, 2019 at 11:17 | comment | added | abx | This is just basic surface theory, nothing particular to do with Kummer surfaces. Just list the fixed points of $\eta$ and $\eta^2$ and look at the action of the group on them. | |
| Jan 29, 2019 at 10:42 | history | asked | Soby | CC BY-SA 4.0 |