Research:
Algebraic geometry (higher dimensional, birational, minimal model program).
Papers:
Singularities of linear systems and boundedness of Fano varieties, 2016
Anti-pluricanonical systems on Fano varieties, 2016
Iitaka's Cn,m conjecture for 3-folds over finite fields, 2015
(Joint with Yifei Chen and Lei Zhang)
Existence of Mori fibre spaces for 3-folds in char p, 2014.
(Joint with Joe Waldron)
Effetivity of Iitaka fibrations and pluricanonical systems of polarized pairs, 2014.
To appear in Pub. Math. IHES. (Joint with De-Qi Zhang)
The augmented base locus of real divisors over arbitrary fields, 2013.
To appear in Math. Annalen.
Varieties fibred over abelian varieties with fibres of log general type, 2013.
Advances in Math. Volume 270 (2015), 206–222. (joint with Jungkai Chen)
Existence of flips and minimal models for 3-folds in char p, 2013.
To appear in Annales scientifiques de l'ENS.
Log canonical pairs with good augmented base loci, 2013.
Compositio Math. Volume 150 (2014), 579-592. (joint with Zhengyu Hu)
Polarized pairs, log minimal models, and Zariski decompositions (original title was: On log minimal models and Zariski decompositions II), 2013.
Nagoya Math. J. Volume 215 (2014), 203-224. (joint with Zhengyu Hu)
Singularities on the base of a Fano type fibration, 2012.
To appear in J. Reine Angew Math.
Images of manifolds with semi-ample anti-canonical divisor (this appeared on arxiv as "On the moduli part of the Kawamata-Kodaira canonical bundle formula").
To appear in Journal of Algebraic Geometry. (joint with Yifei Chen)
Divisorial algebras and modules on schemes, 2011.
A
short version
appeared in J. Math. Soc. Japan Volume 65, Number 4 (2013), 1319-1328.
Existence of log canonical flips and a special LMMP.
Pub. Math. IHES. Volume 115 (2012), Issue 1, 325-368.
Supplement to the paper "On existence of log minimal models II", 2011.
This paper appears as a section of the previous paper.
On existence of log minimal models and weak Zariski decompositions,
Math Annalen, Volume 354 (2012), Number 2, 787-799.
On existence of log minimal models II,
J. Reine Angew Math. 658 (2011), 99-113.
Minimal models, flips and finite generation : a tribute to V.V. SHOKUROV and Y.-T. SIU,
In "Classification of algebraic varieties", European Math Society series of congress reports (2010)
(joint with Mihai Paun)
Iitaka conjecture C_{n,m} in dimension six
.
Compositio Math. volume 145 (2009), 1442-1446.
On termination of log flips in dimension four.
Math. Ann. volume 346, no 2 (2009), 251-257.
Log minimal models according to Shokurov.
J. Algebra and Number Theory, volume 3, no 8 (2009), 951-958.
On existence of log minimal models.
Compositio Mathematica 146 (2010), 919-928.
Existence of minimal models for varieties of log general type.
(joint with Cascini, Hacon and M
^{c}
Kernan)
J. Amer. Math. Soc. 23 (2010), 405-468.
Mld's vs thresholds and flips.
(joint with Shokurov).
J. Reine Angew Math, 638 (2010), 209-234.
Ascending chain condition for log canonical thresholds and termination of log flips.
Duke Math. J. Volume 136, Number 1 (2007), 173-180.
PhD thesis,
2004
Boundedness of epsilon-lc complements on surfaces II,
2004
Boundedness of epsilon-lc complements on surfaces,
2004
On Shokurov's log flips: the 3-dimensional case,
2002
Elements of nonstandard algebraic geometry,
2001
Talks:
Minimal model program and moduli spaces,
2007
(Hokkaido University, Japan)
A complete list of talks
(up to October 2011)