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

Abstract

We prove sharp ${\ell }^2$-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.

24 pages, in the present version the exposition reflects that Cor 1.4 was already obtained by T. Wooley in [16]