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2019 NCTS Mini-courses in Algebraic Geometry
15:30 - 17:20 on Wednesdays and Fridays, October 2 - November 1, 2019
R440, Astronomy-Mathematics Building, NTU

Keiji Ogiso (University of Tokyo)
Yujiro Kawamata (University of Tokyo & NCTS)

Jungkai Chen (National Taiwan University & NCTS)

一、 課程背景與目的:
The purpose of this event is to provide an introduction to some interesting and important topics in algebraic geometry. 
二、 課程之大綱:
Series I:
Lecturer: Keiji Oguiso (Tokyo/NCTS)
Title: Finite generation problem of the discrete automorphism group of a smooth projective variety and related problems
Abstract: It is natural to ask if the quotient group of the automorphism group of a smooth complex projective variety by the identity component is finitely generated. Or more specifically, the automorphism group of a smooth projective variety is finitely generated if it is discrete.
The answer is clearly affirmative in dimension one and is known to be affirmative for long time for minimal surfaces (in the classical sense), both of which I will explain in my lecture with needed materials such as finiteness of pluricanonical representaion with proof,  but surprizingly, it is quite recent (2018-2019) that negative answers are given, first in dimension $6$ by Lesieutre and then
by Dinh and me in any dimension $ge 2$.
In my lectures, I would like to explain our negative answer and further progress eg. in positive characteristic phenomena, and closely related probems such as finiteness of real forms and Kawamata-Morrison cone conjectue so on with proofs.
I assume audience has some familiarity with the classification result of projective surfaces and, at a few places, Torelli Theorem for K3 surfaces and the liftability of K3 surfaces to characteritic zero (Deligne's theorem), while I explicitly state them in my lectures. I will also mention main references/sources during my lectures. 
Series II:
Lecturer: Yujiro Kawamata (Tokyo/NCTS)
Title: On non-commutative deformations and A-infinity algebras.
Abstract: I will explain descriptions of versal non-commutative deformations of sheaves using A-infinity algebras. I will also explain the convergence and algebraicity of deformation algebras.
三、 課程詳細時間地點 :
I-1 10/2(Wed)  15:30-17:20
I-2 10/9 (Wed) 15:30-17:20
I-3 10/16 (Wed) 15:30-17:20
I-4 10/25 (Wed) 15:30-17:20
II-1 10/18 (Fri) 15:30-17:20
II-2 10/25 (Fri) 15:30-17:20
II-3 11/1 (Fri) 15:30-17:20

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