研究概要 |
代数多様体の標準因子に注目した幾何学を研究している. 特に高次元代数幾何学で最も重要な予想の一つであるアバンダンス予想と呼ばれるものを研究している. また、(半)対数的標準対, 標準因子公式, 準随伴公式, 対数的Fano多様体, 正標数還元技術の応用なども研究してきた.
|
主要論文 |
- "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.
|