ScalingStacks

Remark 4 [03X7]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

Remark 4

For B=S2B=S^{2} and Bs​i​n​g={x1,…,x24}B^{sing}=\{x_{1},\dots,x_{24}\} with the standard singular 𝐙{\bf Z}-affine structure we have constructed a KK-analytic K3 surface depending on 2020 parameters in K×K^{\times}. More precisely, we have a 2020-dimensional KK-analytic space of conjugacy classes of representations

π1​(S2∖Bs​i​n​g)→S​L​(2,𝐙)⋉(K×)2\pi_{1}(S^{2}\setminus B^{sing})\to SL(2,{{\bf Z}})\ltimes(K^{\times})^{2}

such that the monodromy around each singular point is conjugate to the pair (A,(1,1))(A,(1,1)) where A∈S​L​(2,𝐙)A\in SL(2,{{\bf Z}}) is equal to

(1101).\left(\begin{array}[]{cc}1&1\\ 0&1\end{array}\right)\,\,.

(compare with Section 3.3).

Original mathematics by the credited authors. Source-backed reader collection; mathematical self-containment is not assessed.