IUMJ

Title: Extended shockwave decomposability related to boundaries of holomorphic 1-chains within $\mathbb{CP}^2$

Authors: Ronald A. Walker

Issue: Volume 57 (2008), Issue 3, 1133-1172

Abstract:

We consider the notion of meromorphic Whitney multifunction solutions to $ff_{\xi} = f_{\eta}$, which yields an enhanced version of the Dolbeault Henkin characterization of boundaries ofholomorphic 1-chains within $\mathbb{C}\mathbb{P}^2$. By analyzing the equations describing meromorphic Whitney multifunction solutions to $ff_{\xi} = f_{\eta}$ and by creating some generalizationsof certain linear dependence results, we show that a function $G$ may be decomposed into a sum of such solutions, modulo $\xi$-affine functions and with a selected bound on the degree of such sum, if and only if $G_{\xi\xi}$ satisfies a finite set of explicitly constructible partial differential equations.