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Classification of Kuga fiber varieties

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Author(s): Salman Abdulali
Year: 2022

Language: English
Pages: 19
Tags: Hodge theory, algebraic geometry

Classification of Kuga fiber varieties
1 Introduction
2 Kuga fiber varieties
2.1 Groups of hermitian type
2.2 Equivariant holomorphic maps
2.3 The Siegel space
2.4 The fiber varieties
3 Satake’s classification
3.1 Necessary conditions
3.2 A sufficient condition
3.3 More on type I
4 Chemistry and rigidity
4.1 Chemistry
4.2 The space of equivariant maps
5 The rigid case
5.1 Statement of the theorem
5.2 Beginning of the proof
5.3 Construction of the complex structure
5.4 Construction of symmetric forms
5.5 The symmetric form and the complex structure
5.6 Construction of an alternating form
5.7 Properties of the complex structure
5.8 Conclusion of the proof
6 The general case
7 An example
References