| Project/Area Number |
18340010
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kobe University |
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Principal Investigator |
YOSHIOKA Kota Kobe University, 理学研究科, 教授 (40274047)
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| Co-Investigator(Kenkyū-buntansha) |
SAITO Masahiko 神戸大学, 理学研究科, 教授 (80183044)
YAMADA Yasuhiko 神戸大学, 理学研究科, 教授 (00202383)
NOUMI Masatoshi 神戸大学, 自然科学系先端融合研究環重点研究部, 教授 (80164672)
中島 啓 京都大学, 大学院・理学研究科, 教授 (00201666)
松下 大介 北海道大学, 理学研究科, 准教授 (90333591)
稲場 道明 京都大学, 大学院・理学研究科, 講師 (80359934)
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| Co-Investigator(Renkei-kenkyūsha) |
NAKAJIMA Hiraku 京都大学, 数理解析研究所, 教授 (00201666)
MASTUSHITA Daisuke 北海道大学, 理学研究院, 准教授 (90333591)
INABA Michiaki 京都大学, 理学研究科, 講師 (80359934)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥17,110,000 (Direct Cost: ¥13,900,000、Indirect Cost: ¥3,210,000)
Fiscal Year 2009: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2008: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2007: ¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2006: ¥3,200,000 (Direct Cost: ¥3,200,000)
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| Keywords | ベクトル束 / Donaldson不変量 / モジュライ / Donaldson 不変量 / フーリエ向井変換 |
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| Research Abstract |
We derived the wall crossing formula and the blow-up formula of the Donaldson invariants. We also formulated K-theoretic analogue of the Doinaldson invariants and got the wall crossing formula. We studied the betation of the Fourier-Mukai transform and the stability condition ang got a nice result. As an application, we also studied the moduli of stable sheaves on abelian surfaces.
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