| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Research Abstract |
The goal of this research project was to give an affirmative answer to Schwede-Smith's conjecture, which says that a projective variety X over an algebraically closed field of characteristic zero is log Fano if and only if its modulo p reduction is globally F-regular for sufficiently large p. We proved that the conjecture holds true when X is a Mori dream space or a surface. Under the same assumption, that is, when X is a Mori dream space or a surface, we also proved that if its modulo p reduction is globally F-split for infinitely many p, then X is log Calabi-Yau.
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