Moduli of K-stable Varieties
Giulio / Dervan Codogni
Résumé
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 Kahler 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 Kahler and almost-Kahler 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 Kahler-Einstein metrics.
1 F. Ambro and J. Kollar, Minimal Models of semi-log-canonical pairs.- 2 G. Codogni and J. Stoppa, Torus Equivariant K-stability.- 3 K. Fujita, Notes on K-semistability of topic polarized surfaces.- 4 E. Legendre, A note on extremal toric almost Kahler metrics.- 5 Y. Odaka, Tropical geometric compactification of moduli, I - M_g case.- 6 Z. Sjoestroem Dyrefelt, A partial comparison of stability notions in Kahler geometry.- 7 C. Spotti, Kahler-Einstein metrics via moduli continuity.- 8 X. Wang, GIT stability, K-stability and moduli space of Fano varieties.
Ruadhai Dervan received his PhD from the University of Cambridge in 2016, and is currently a Research Fellow at Gonville & Caius College, Cambridge. His research focuses on complex geometry and algebraic geometry, especially canonical Kahler metrics, moduli theory and geometric analysis.
Giulio Codogni obtained his PhD from the University of Cambridge in 2016, and is currently a Research Fellow at the Department of Mathematics and Physics, Roma Tre University. His research interests are in algebraic geometry, especially K-stability, moduli theory and modular forms.
Filippo Viviani received his PhD from the University of Roma Tor Vergata in 2007, and is currently an Associate Professor at Roma Tre University. His research focuses on algebraic geometry, especially moduli theory and its connections with birational geometry and combinatorics.
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Springer |
| Auteur(s) | Giulio / Dervan Codogni |
| Parution | 06/08/2019 |
| Nb. de pages | 181 |
| EAN13 | 9783030131579 |
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