Moishezon Morphism Seminar Note
Published:
The purpose of this series of notes is to discuss the recent paper Moishezon morphism by Professor Kollár in detail. Let us first briefly answer the question WHY Moishezon?
First, Moishezon spaces have more functorial behavior (compared with projective varieties), as we will see in my notes. Secondly, from almost any projective variety we can construct a Moishezon space via bimeromorphic modification, making Moishezon spaces versatile in birational geometry. Thirdly, by Artin’s fundamental theorem, the category of Moishezon spaces appears naturally in moduli theory. Another compelling reason to consider the Moishezon category is that it allows cutand-paste operations similar to those we can perform in topology.
Here is the outline:
1. Basic Properties of Moishezon Varieties and Moishezon Morphisms [update 7.4]
2. Fiberwise Bimeromorphic Maps [update 7.4]
3. General Type Locus and Moishezon Locus [update 7.4]
4. Projectivity Criteria and Projective Locus [update 7.4]
5. Rational Curves on Moishezon Spaces, Mori Bend-and-Break for Moishezon Varieties [update 7.4]
6. Algebraic Approximation and Inversion of Adjunction [TODO]
Summary Slides [update 12.4]
Merged: Notes on Moishezon Morphisms