| Project/Area Number |
24740004
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Takagi Hiromichi 東京大学, 大学院数理科学研究科, 准教授 (30322150)
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | Fano variety / rationality of moduli / Key variety / Calabi-Yau variety / Reye congruence / Enriques surface / quartic double solid / 慨del Pezzo 3-fold / theta characteristic / Fano多様体 / Q-Fano 3-fold / 端射線の理論 / 一般型曲面 / 非有理的多様体 / Reye合同型Enriques曲面 / ホモロジー的射影双対 / 導来圏の半直交分解 / ホモロジー的射影双対性 / Artin-Mumford二重立体 / Enriques-Fano 3-fold / 直交線形切断 / Calabi-Yau ３様体 / 導来圏 / ミラー対称性 / Sarkisov リンク |
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| Outline of Final Research Achievements |
With Shinobu Hosono, I studied Calabi-Yau 3-folds of Reye congruences about their projective geometry, mirror symmetry, and derived category. With him, I also established the relation between the derived categories of Enriques surfaces of Reye congruences and Artin-Mumford double solids.With Francesco Zucconi,we constructed a theory giving a relation between the moduli space of rational curves on the quintic del Pezzo 3-fold and that of spin curves. Based on this,I showed that the following moduli spaces are rational: (1) The moduli space of genus 4 spin curves (2) The moduli spaces of triplets (C,p,s), where C is a curve of genus not less than 2, p is a point of C, and s is a theta characteristic on C without global section.
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