Timeline for Genus=2 theta functions, Arnold's relation, and KZ connection
Current License: CC BY-SA 3.0
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| Apr 24, 2018 at 8:50 | comment | added | Dan Petersen | @inkspot Very nice! A remark is that taking dlog of a cross-ratio gives a sum of four "Arnold forms" $w_{ij}$. Moreover the dlog's of cross-ratios can be used to give an alternative presentation of the cohomology ring of $M_{0,n} = C_{n-1}/G$, analogous to Arnolds presentation of the cohomology ring of $C_n$. See Section 2 of my joint paper with Johan Alm arxiv.org/abs/1509.09274 | |
| Apr 23, 2018 at 17:40 | comment | added | inkspot | Thomae's formula (Mumford, Tata Lectures on Theta II) relates the cross-ratios of the branch points $z_1,...,z_5,\infty$ to fourth powers of the theta-nulls. However, anything pulled back from $\mathcal A_2[2]$ will be $G$-invariant, so finding the individual $z_i-z_j$ seems to me to be excluded. | |
| Apr 23, 2018 at 16:39 | history | edited | shehryar sikander | CC BY-SA 3.0 |
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| Apr 23, 2018 at 16:29 | history | edited | shehryar sikander | CC BY-SA 3.0 |
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| Apr 23, 2018 at 16:06 | history | edited | shehryar sikander |
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| Apr 23, 2018 at 16:00 | history | edited | shehryar sikander | CC BY-SA 3.0 |
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| Apr 23, 2018 at 15:48 | history | edited | shehryar sikander | CC BY-SA 3.0 |
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| Apr 23, 2018 at 15:43 | comment | added | shehryar sikander | Thanks for the comment. Indeed, I meant which theta functions pull back to functions $(z_i-z_j)$ on $C_5$, then the logarithmic derivatives of such theta functions would correspond to the differential forms $d log (z_i- z_j)$ and should satisfy the Arnold relation. I'll make the edit in my question. | |
| Apr 22, 2018 at 21:42 | history | edited | shehryar sikander | CC BY-SA 3.0 |
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| Apr 22, 2018 at 21:13 | review | First posts | |||
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| Apr 22, 2018 at 21:13 | history | asked | shehryar sikander | CC BY-SA 3.0 |