Li Yi

Li Yi

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

Birational Geometry Note: Rationality Problems in Birational Geometry

less than 1 minute read

Published:

The aim of this note is try to summarize the rationality problems in birational geometry.

Here is the outline of the notes:

Part I. A Survey on Birational Invariants

Birational Invariance plays a central role in the study of rationality problems. In the first part, we will survey the old and new birational invariance.

Note I.1. Intermediate Jacobian

Note I.2 Motivic Invariance

Note I.3 Stable birational Invariance

Note I.4 Burnside Ring

Note I.5 Hodge atom

Note I.6 Structure of Birational Automorphism

Part II. Geometry of Rational Curves

Note II.1 Mori theory on rational curves,

Note II.2 Rational curves on Kahler variety,

Note II.3 Smooth of chain of rational curves,

Part II. Structure of Mori Fiber Space

Note II.1 Sarkisov program,

Part III. Structure theorem for Rational connected varieties

Note III.1 GHS theorem for rational connected varieties,

Note III.2 Rationally connectedness of Fano varieties,

Note III.3 On Shokurov rationality conjecture,

Part IV. Basic properties of uniruled varieties

Note Deformation of uniruled varieties,

Part V. Rationality Criterion

Part V.1 Stable rationality and decomposition of diagonal,

10. Cubic hypersurfaces,

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