Li Yi

Li Yi

I am a 3rd year PhD student majoring in birational geometry

Birational Geometry Note: Adjunction Theory

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The aim of this note is to introduce adjunction theory in birational geometry. Among the various techniques in birational geometry, adjunction theory is one of the most powerful tools. It allows us to relate the geometry — particularly the singularities — of an ambient variety to those of suitable subvarieties.

A useful summary can be found in Anti-pluricanonical systems on Fano varieties, Chapter 3). This note is based on that paper, and our goal is to provide a more detailed introduction to adjunction theory.

Part I. Canonical Bundle Formula

For detailed information see my reading notes

1. Adjunction Formulas.

2. Kawamata’s canonical bundle formula [6.4]

3. Ambro’s canonical bundle formula

4. Fujino-Mori canonical bundle formula

5. Generalized canonical bundle formula of Birkar-Zhang [6.7]

6. Canonical bundle formula for generalized Kahler pairs [6.4]

7. Kawamata’s subadjunction formula

8. Hacon-Mckernan-Xu’s subadjunction type theorem [6.6]

9. Inversion of Adjunction

10. Applications of cyclic covering trick

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