Current research
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I am studying a geometry which is remarked by the canonical divisor of algebraic varieties. Particularly I am studying the abundance conjecture which is one of the most important conjecture in higher dimensional algebraic geometry. I also have studied (semi-) log canonical pairs, canonical bundle formulae, subadjunctions, log Fano varieties, applications of the reduction modulo positive characteristics techniques, and so on.
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Selected publications
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- "On weak Fano varieties with log canonical singularities", J. Reine Angew. Math. 665 (2012), 237--252
- "Abundance theorem for numerically trivial log canonical divisors of semi-log canonical pairs" J. Algebraic Geom. 22 (2013), 549--564,
- (with Osamu Fujino)"On canonical bundle formulas and subadjunctions" Michigan Math. J. 60, (2012), no. 3, 255--264.,
- "On the minimal model theory for dlt pairs of numerical log Kodaira dimension zero.", Math. Res. Lett. 18 (2011), no. 5, 991--1000,
- (with Brian Lehmann) "Reduction maps and minimal model theory",
Compositio Math. 149, (2013) No.2, 295--308.,
- (with Osamu Fujino) "Log pluricanonical representations and the
abundance conjecture" Compositio Math. 150, No.4, (2014) 593--620.
- (with Shinnosuke Okawa, Akiyoshi Sannai, Shunsuke Takagi) "
Characterizaton of varieties of Fano type via singularities of Cox rings" J. Algebraic Geom. 24 (2015), no.1, 159--182.
- "Remarks on the non-vanishing conjecture", Algebraic geometry in East Asia--Taipei 2011, Adv. Stud. Pure Math., 65, Math. Soc. Japan, Tokyo, 2014.
- (with Paolo Cascini) "On the anti-canonical ring and varieties of Fano type" Saitama Math. J. Vol. 30 (2013), 27--38.
- (with Osamu Fujino) "On the moduli b-divisors of lc-trivial
fibrations" Annales de l'institut Fourier, 64 no. 4 (2014), 1721--1735.
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Memberships, activities and
Awards
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The Mathematical Society of Japan
MSJ Takebe Katahiro Prize for Encouragement of Young Researchers(2011)
The second JSPS Ikushi Prize (2012)
The University of Tokyo President's Prize(2012)
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