Decoupling for complex curves and improved decoupling for the cubic moment curve

We prove sharp ${\mathrm{\ell }}^2$-decoupling inequalities for non-degenerate complex curves via the bilinear argument due to Guo–Li–Yung–Zorin-Kranich, which in turn is inspired by the efficient congruencing argument of Wooley. Secondly, quantifying the iteration in the cubic case, we obtain a logarithmic refinement of the decoupling inequality for the cubic moment curve.