Lectures On Counterexamples In Several Complex Variables

Lectures on Counterexamples in Several Complex Variables

Counterexamples are remarkably effective for understanding the meaning, and the limitations, of mathematical results. Fornss and Stensnes look at some of the major ideas of several complex variables by considering counterexamples to what might seem like reasonable variations or generalizations. The first part of the book reviews some of the basics of the theory, in a self-contained introduction to several complex variables. The counterexamples cover a variety of important topics: the Levi problem, plurisubharmonic functions, Monge-Ampre equations, CR geometry, function theory, and the $barpartial$ equation. The book would be an excellent supplement to a graduate course on several complex variables.