Timeline for Topology of theta nulls
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2017 at 0:55 | vote | accept | Kevin | ||
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Nov 2, 2015 at 16:27 | answer | added | Curtis McMullen | timeline score: 5 | |
| Jul 1, 2012 at 23:17 | comment | added | JHM | Your 'theta-null' $\Theta(\Omega, 0)$ is the usual theta function one would associate to the quadratic form $x \mapsto {}^t x \Omega x$. Cf. Conway/Sloane's "Sphere Packings, Lattices, and Groups" to see how theta functions of lattices can actually be used. For instance, C/S derive almost all the basic properties on the Leech lattice via its theta function. | |
| Jul 1, 2012 at 23:11 | comment | added | JHM | It appears to me that almost nothing is really known about theta functions $\Theta(\Omega, z)$. Even the (full!) functional equation wrt the $Sp(2g, \mathbb{Z})$ action remains opaque (cf. Mumford's Tata Lectures III). For instance, for given $\Omega \in \mathfrak{h}_{g}$ set $Z[\Omega]$ to be the zero locus of $\Theta(\Omega, \cdot)$ in $\mathbb{C}^{g}$, ie. the theta divisor. Then I don't think anyone has a decent description of the orbits $Z[\Omega.\gamma]$ for $\gamma \in Sp(2g, \mathbb{Z})$. Ie. is the theta divisor even equivariant? | |
| Jul 1, 2012 at 22:04 | history | asked | Kevin | CC BY-SA 3.0 |