2 problems

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Rank conjecture for the restricted ramification divisor map
Rank conjecture. The rank of the complex derivative of $\rho$ at $(i_1,i_2)$ satisfies:
Conjectureopencone-spherical-metrics ramification-divisors riemann-surfacesarXiv posted 2 days ago
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Existence of strictly polystable extensions for generic line bundles
Existence conjecture. There exists a strictly polystable extension of $L^{-1}$ by $L$ . This would extend the existence results for reducible cone spherical metrics to generic line…
Conjectureopencone-spherical-metrics riemann-surfaces vector-bundlesarXiv posted 2 days ago

Rank conjecture for the restricted ramification divisor map