We report on numerical and experimental studies showing the influence of arc curvature on the confinement loss in hypocycloid-core Kagome hollow-core photonic crystal fiber. The results prove that with such a design the optical performances are strongly driven by the contour negative curvature of the core-cladding interface. They show that the increase in arc curvature results in a strong decrease in both the confinement loss and the optical power overlap between the core mode and the silica core-surround, including a modal content approaching true single-mode guidance. Fibers with enhanced negative curvature were then fabricated with a record loss-level of 17 dB/km at 1064 nm.