Timeline for Simplest examples of nonisomorphic complex algebraic varieties with isomorphic analytifications
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 24, 2011 at 18:31 | comment | added | Ravi Vakil | I should have added: Torsten's comment reminds me that I forgot another valuable metric: one with a simple conceptual underpinning. | |
| Jun 24, 2011 at 18:29 | comment | added | Ravi Vakil | I found both this example enlightening, and also Torsten Ekedahl's conceptual explanation --- thanks! | |
| Jun 23, 2011 at 8:07 | comment | added | naf | @ACL. I was aware of this; my answer was posted before his... | |
| Jun 23, 2011 at 7:27 | comment | added | ACL | In fact, this example is the same as Georges's one! Indeed, the universal vector extension of an elliptic curve (used there) can be interpreted as the moduli space of line bundles with integrable connections on the (dual) elliptic curve. | |
| Jun 21, 2011 at 19:51 | comment | added | Torsten Ekedahl | This is clearly the most conceptual way to present this example but measure 1 is increased if one notices that we are dealing with the quotient of $\mathbb C^2$ by the group of translations generated by $(1,0)$ and $(\tau,1)$. On the one hand the quotient is an $\mathbb A^1$-torsor over $\mathbb C/(\mathbb Z 1+\mathbb Z\tau$ (and thus algebraic), on the other hand a $2$-dimensional complex vector space divided by the subgroup generated by a basis, i.e., $(\mathbb C^\times)^2$ which itself is algebraic. | |
| Jun 21, 2011 at 19:09 | history | answered | naf | CC BY-SA 3.0 |