Li Yi

Li Yi

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

Birational Geometry and Deformation Theory

1 minute read

Published:

The aim of this series of notes is to give a brief introduction to the basics of deformation theory, and then to focus on its applications to certain problems in birational geometry.

Part III. Invariance of plurigenera problems

Note-1 Levine’s deformation theoretical method to invariance of plurigenera problem [update 8.12]

Note-2 Levine and Fujiki’s approach to Deformation invariance of uniruled varieties [update 8.12]

Note-3 Nakayama’s invariance of plurigenera results [update 8.15]

Note-4 Algebraic proof of invariance of plurigenera with general type assumption

Note-5 Paun-Demailly’s analytic proof of invariance of plurigenera [update 8.25]

Note-6 Hacon-Mckernan-Xu’s log invariance of plurigenera

Note-4 Takayama’s proof of invariance of plurigenera

Note-5 Kollar’s MMP proof of invariance of plurigenera

Note-6 Deformation invariance of numerical Kodaira dimension of Nakayama

Note-7 Cao-Paun’s approach to invariance of plurigenera

Note-8 Applications of invariance of plurigenera

Part IV. Deformation of Positivities in Birational Geometry

Note-1: Hacon-Mckernan-Xu’s family with good minimal model

Note-2: deFernex-Hacon variation of cones in family

Note-3: Deformation bahavior of projectivity

Part I. Basic knowledge on deformation theory

Note-1: Kodaira-Spencer map, Kodaira-Spencer correspondence,

Note-2: A brief introduction to Obstruction Theory

Note-3: Maurer-Cartan equation, DGLA

Note-4: Bogomolov-Tian-Todorov Theorem, ddbar method and Ran’s T1 lifting theorem with applications

Part II. Deformation of (birational) morphism

Note-1: Blow up in deformation theory

Note-2: Deformation of (rational) curves in complex space

Note-3: Deformation of morphisms

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