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

TL;DR

This paper establishes sharp decoupling inequalities for complex curves using bilinear methods, and refines the decoupling for the cubic moment curve with a logarithmic improvement.

Contribution

It introduces sharp decoupling inequalities for complex curves and provides a logarithmic refinement for the cubic moment curve, advancing decoupling theory.

Findings

Sharp $\, ext{ell}^2$-decoupling inequalities for complex curves.

Logarithmic refinement of 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.