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Moduli of K-stable Varieties

2019-06-27 Mathematics
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Release : 2019-06-27
Genre : Mathematics
Kind : eBook
Book Rating : 580/5 ( reviews)

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Book Synopsis Moduli of K-stable Varieties by : Giulio Codogni

Download or read book Moduli of K-stable Varieties written by Giulio Codogni. This book was released on 2019-06-27. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outcome of the workshop "Moduli of K-stable Varieties", which was held in Rome, Italy in 2017. The content focuses on the existence problem for canonical Kähler metrics and links to the algebro-geometric notion of K-stability. The book includes both surveys on this problem, notably in the case of Fano varieties, and original contributions addressing this and related problems. The papers in the latter group develop the theory of K-stability; explore canonical metrics in the Kähler and almost-Kähler settings; offer new insights into the geometric significance of K-stability; and develop tropical aspects of the moduli space of curves, the singularity theory necessary for higher dimensional moduli theory, and the existence of minimal models. Reflecting the advances made in the area in recent years, the survey articles provide an essential overview of many of the most important findings. The book is intended for all advanced graduate students and researchers who want to learn about recent developments in the theory of moduli space, K-stability and Kähler-Einstein metrics.

Moduli of K-stable Varieties

2019 Differential equations, Partial
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Release : 2019
Genre : Differential equations, Partial
Kind : eBook
Book Rating : 593/5 ( reviews)

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Book Synopsis Moduli of K-stable Varieties by : Giulio Codogni

Download or read book Moduli of K-stable Varieties written by Giulio Codogni. This book was released on 2019. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an outcome of the workshop "Moduli of K-stable Varieties", which was held in Rome, Italy in 2017. The content focuses on the existence problem for canonical Kèahler metrics and links to the algebro-geometric notion of K-stability. The book includes both surveys on this problem, notably in the case of Fano varieties, and original contributions addressing this and related problems. The papers in the latter group develop the theory of K-stability; explore canonical metrics in the Kèahler and almost-Kèahler settings; offer new insights into the geometric significance of K-stability; and develop tropical aspects of the moduli space of curves, the singularity theory necessary for higher dimensional moduli theory, and the existence of minimal models. Reflecting the advances made in the area in recent years, the survey articles provide an essential overview of many of the most important findings. The book is intended for all advanced graduate students and researchers who want to learn about recent developments in the theory of moduli space, K-stability and Kèahler-Einstein metrics.

Families of Varieties of General Type

2023-04-30 Mathematics
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Release : 2023-04-30
Genre : Mathematics
Kind : eBook
Book Rating : 105/5 ( reviews)

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Book Synopsis Families of Varieties of General Type by : János Kollár

Download or read book Families of Varieties of General Type written by János Kollár. This book was released on 2023-04-30. Available in PDF, EPUB and Kindle. Book excerpt: The first complete treatment of the moduli theory of varieties of general type, laying foundations for future research.

Birational Geometry, Kähler–Einstein Metrics and Degenerations

2023-05-23 Mathematics
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Release : 2023-05-23
Genre : Mathematics
Kind : eBook
Book Rating : 599/5 ( reviews)

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Book Synopsis Birational Geometry, Kähler–Einstein Metrics and Degenerations by : Ivan Cheltsov

Download or read book Birational Geometry, Kähler–Einstein Metrics and Degenerations written by Ivan Cheltsov. This book was released on 2023-05-23. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and Pohang The conferences were focused on the following two related problems: • existence of Kähler–Einstein metrics on Fano varieties • degenerations of Fano varieties on which two famous conjectures were recently proved. The first is the famous Borisov–Alexeev–Borisov Conjecture on the boundedness of Fano varieties, proved by Caucher Birkar (for which he was awarded the Fields medal in 2018), and the second one is the (arguably even more famous) Tian–Yau–Donaldson Conjecture on the existence of Kähler–Einstein metrics on (smooth) Fano varieties and K-stability, which was proved by Xiuxiong Chen, Sir Simon Donaldson and Song Sun. The solutions for these longstanding conjectures have opened new directions in birational and Kähler geometries. These research directions generated new interesting mathematical problems, attracting the attention of mathematicians worldwide. These conferences brought together top researchers in both fields (birational geometry and complex geometry) to solve some of these problems and understand the relations between them. The result of this activity is collected in this book, which contains contributions by sixty nine mathematicians, who contributed forty three research and survey papers to this volume. Many of them were participants of the Moscow–Shanghai–Pohang conferences, while the others helped to expand the research breadth of the volume—the diversity of their contributions reflects the vitality of modern Algebraic Geometry.

Moduli Theory and Classification Theory of Algebraic Varieties

2006-11-15 Mathematics
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Release : 2006-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 315/5 ( reviews)

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Book Synopsis Moduli Theory and Classification Theory of Algebraic Varieties by : H. Popp

Download or read book Moduli Theory and Classification Theory of Algebraic Varieties written by H. Popp. This book was released on 2006-11-15. Available in PDF, EPUB and Kindle. Book excerpt:

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