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.

arXiv comment24 pages, in the present version the exposition reflects that Cor 1.4 was already obtained by T. Wooley in [16]