study of commutative rings of positive characteristic using vector bundles

Research Project

Project/Area Number	22540056
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Algebra
Research Institution	Ritsumeikan University
Principal Investigator	TAKAYAMA Yukihide 立命館大学, 理工学部, 教授 (20247810)
Project Period (FY)	2010 – 2012
Project Status	Completed (Fiscal Year 2012)
Budget Amount *help	¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000) Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000) Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000) Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords	代数多様体 / 正標数 / ベクトルバンドル / 小平消滅定理 / 持ち上げ可能性 / 代数幾何学 / Calabi-Yau 3-fold / 代数学 / 可換環論 / 特異点理論 / 双有理幾何学
Research Abstract	I considered the problem whether there exist counter-examples toKodaira type vanishing of cohomoogies for Calabi-Yau 3-folds in positive characteristic.I have studied possibility of constructing the counter-examples via Raynaud-Mukai-s ideaand for the main two examples of unliftable Calabi-Yau 3-fods I showed that Kodaira typevanishing holds to some extent.