Buch, Englisch, Band 41, 220 Seiten, Format (B × H): 170 mm x 240 mm, Gewicht: 382 g
Reihe: Oberwolfach Seminars
Buch, Englisch, Band 41, 220 Seiten, Format (B × H): 170 mm x 240 mm, Gewicht: 382 g
Reihe: Oberwolfach Seminars
ISBN: 978-3-0346-0289-1
Verlag: Birkhäuser Basel
This book grew out of the Oberwolfach-SeminarHigherDimensionalAlgebraicGeo- tryorganizedbythetwoauthorsinOctober2008. Theaimoftheseminarwas tointroduce advanced PhD students and young researchers to recent advances and research topics in higher dimensional algebraic geometry. The main emphasis was on the minimal model program and on the theory of moduli spaces. The authors would like to thank the Mathematishes Forshunginstitut Oberwolfach for its hospitality and for making the above mentioned seminar possible, the participants to the seminar for their useful comments, and Alex Küronya, Max Lieblich, and Karl Schwede for valuable suggestions and conversations. The ?rst named author was partially supported by the National Science Foundation under grant number DMS-0757897 and would like to thank Aleksandra, Stefan, Ana, Sasha, Kristina and Daniela Jovanovic-Haconfor their love and continuos support. The second named author was partially supported by the National Science Foun- tion under grant numbers DMS-0554697 and DMS-0856185, and the Craig McKibben and Sarah Merner Endowed Professorship in Mathematics at the University of Wa- ington. He would also like to thank Tímea Tihanyi for her enduring love and support throughout and beyond this project and his other co-authors for their patience and und- standing. Contents I Basics 1 1INTRODUCTION 3 1. A. CLASSIFICATION 3 2PRELIMINARIES 17 2. A. NOTATION 17 2. B. DIVISORS 18 2. C. REFLEXIVE SHEAVES 20 2. D. CYCLIC COVERS 21 2. E. R-DIVISORS IN THE RELATIVE SETTING 22 2. F. FAMILIES AND BASE CHANGE 24 2. G. PARAMETER SPACES AND DEFORMATIONS OF FAMILIES 25 3SINGULARITIES 27 3. A.
Zielgruppe
Research
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Weitere Infos & Material
Basics.- Preliminaries.- Singularities.- Recent advances in the minimal model program.- The main result.- Multiplier ideal sheaves.- Finite generation of the restricted algebra.- Log terminal models.- Non-vanishing.- Finiteness of log terminal models.- Compact moduli spaces of canonically polarized varieties.- Moduli problems.- Hilbert schemes.- The construction of the moduli space.- Families and moduli functors.- Singularities of stable varieties.- Subvarieties of moduli spaces.
