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課程名稱 |
代數幾何專題：凝聚層的導出範疇
Derived categories of coherent sheaves |
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開課學期 |
110-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
林學庸 |
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課號 |
MATH5275 |
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課程識別碼 |
221 U9200 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期二2,3,4(9:10~12:10) |
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上課地點 |
天數101 |
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備註 |
總人數上限：40人 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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課程概述 |
Derived categories of abelian categories were introduced and developed by Grothendieck and Verdier in the 60s. In algebraic geometry, derived categories of coherent sheaves are among the most fundamental and refined invariants of projective varieties. Since the foundational works of Mukai, Bondal-Orlov, and Kontsevich from the 80s and early 90s, the study of such invariants has been very much motivated by the birational geometry of projective varieties and (non disjointly) homological mirror symmetry. |
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課程目標 |
We will start with the basics of derived categories including semi-orthogonal decompositions and Fourier-Mukai transforms. Later in the course we plan to discuss some recent developments related to derived categories of coherent sheaves, such as homological projective duality, stability conditions, noncommutative crepant resolutions, or derived categories and GIT. |
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課程要求 |
We will assume knowledge of derived functors, (quasi)-cohenet sheaves and their cohomology. One reference is
https://math.stanford.edu/~vakil/216blog/FOAGnov1817public.pdf
Chapters 1, 2, 13-18, 23, 28, 30. |
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預期每週課後學習時數 |
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Office Hours |
每週四 09:00~10:00 |
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指定閱讀 |
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參考書目 |
There is no required reference. A first reference covering the basics of derived categories of coherent sheaves is
D. Huybrechts: Fourier-Mukai Transforms in Algebraic Geometry
(https://typo.iwr.uni-heidelberg.de/fileadmin/groups/arithgeo/templates/data/Judith_Ludwig/Derivierte_Kategorien/H.pdf)
We will provide further references during the semester. |
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評量方式
(僅供參考) |
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