Higher Dimensional Geometry (2015 Fall)  

This is the second semester of a one year class on higher dimensional geometry. For the information of the first semester, see here. 

We will discuss more advanced topics including the proof of the finite generation of pluricanonical rings. 

Prerequisite

Being familiar with the first three chapters of [KM98].

Reference

[BCHM] Birkar, Cascini, Hacon, McKernan: Existence of minimal models for varieties of log general type.

[CL12] Cascini, Paolo; Lazic, Vladimir: New Outlook on the Minimal Model Program I.

[Cor07] Corti, Alessio: Flips for 3 folds and 4-folds.

[Kol97] Kollár, János; Singularity of Pairs. 

[KM98] Kollár, János; Mori, Shigefumi; Birational geometry of algebraic varieties.  Section 1-3. 

[Kol08] Kollár, János; Exercises in the birational geometry of algebraic varieties. arXiv:0809.2579. 

[HM10] Hacon, McKernan: Flips and flops. Proceedings of the International Congress of Mathematicians. Volume II, 513–539

[Laz04] Lazarsfeld, Robert; Positivity in algebraic geometry I, II.

Classroom/Schedule

一教208 Tuesday 3:10-6:00pm  

Syllabus

9.15: Plt singularities. ([Cor07], Chapter 3) 

9.22: Three dimensional case. ([Cor07], Chapter 2) 

9.29: On termination of flips. ([Cor07], Chapter 4 and [HM10]) 

10.13: Multiplier ideals and Siu’s proof on invariance of plurigenera. ([Laz04], 11.5)

10.20: Hacon-McKernan’s extension theorem I. ([Cor07], Chapter 5 and [CL12], Section 3)

10.27: Hacon-McKernan’s extension theorem II. ([Cor07], Chapter 5 and [CL12], Section 3)

11.1-11.28: Prof. Colliot-Thelene will teach ‘Brauer groups of schemes’ in this month. See here.

12.8: Results in [BCHM]. 

12.14 (镜春园 82J04, 10am-1pm Special time): Special finiteness ([BCHM], Section 4)

12.22: Special termination and non-vanishing ([BCHM], Section 5 and 6)

12.29: Finiteness of models, further results. ([BCHM], Section 7)