25.2 Historical notes4D6830B53C70

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Local regularization and products provide a common starting point for the results of this book. A smooth local correction makes these methods available for nonclosed backgrounds, including on Kähler manifolds. Global arguments must distinguish a closed class on a non-Kähler manifold from a nonclosed background: the former may lack the Kähler positivity used in classical existence theorems, while the latter loses the cohomological control of Monge–Ampère masses. Gauduchon duality, relative envelopes and the available mass bounds connect the sources discussed below. Their hypotheses also decide whether a solution keeps the ordinary singularity type of its reference or belongs only to its relative envelope class.

These notes identify the sources of the results of the book, with precise locators, and explain how the arguments given in the book relate to the original ones. Indications such as v1 or arXiv version in a locator refer to the version of the source that was used. Where needed, the conversion from the normalization of $\mathrm{dd}^{\mathrm{c}}$ or of the Chern–Ricci form used in a source to the conventions fixed at the beginning of the book is indicated next to the citation.