The blow-up energy of super-Liouville systems on surfaces with conical boundary singularities is quantized: interior regular points contribute 4π, boundary regular points 2π, and conical points contribute 4π(1+α) or 2π(1+α).
Bartolucci, A compactness result for periodic multivortices in the electroweak theory , Nonlinear Analysis 53 (2003) 277-297
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Energy quantization for a singular super-Liouville boundary value problem
The blow-up energy of super-Liouville systems on surfaces with conical boundary singularities is quantized: interior regular points contribute 4π, boundary regular points 2π, and conical points contribute 4π(1+α) or 2π(1+α).