Subadjunction for Quasi-Log Canonical Pairs and Its Applications

[BCHM] C. Birkar, P. Cascini, C. D. Hacon, J. McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010), no. 2, 405–468.

[F1] O. Fujino, Theory of non-lc ideal sheaves: basic properties, Kyoto J. Math. 50 (2010), no. 2, 225–245.

[F2] O. Fujino, Fundamental theorems for the log minimal model program, Publ. Res. Inst. Math. Sci. 47 (2011), no. 3, 727–789.

[F3] O. Fujino, Fundamental theorems for semi log canonical pairs, Algebr. Geom. 1 (2014), no. 2, 194–228.

[F4] O. Fujino, Foundations of the minimal model program, MSJ Memoirs, 35. Mathemat- ical Society of Japan, Tokyo, 2017.

[F5] O. Fujino, Pull-back of quasi-log structures, Publ. Res. Inst. Math. Sci. 53 (2017), no. 2, 241–259.

[F6] O. Fujino, Fundamental properties of basic slc-trivial fibrations, to appear in Publ. Res. Inst. Math. Sci.

[F7] O. Fujino, Cone theorem and Mori hyperbolicity, preprint (2020).

[FF] O. Fujino, T. Fujisawa, Variations of mixed Hodge structure and semipositivity theo- rems, Publ. Res. Inst. Math. Sci. 50 (2014), no. 4, 589–661.

[FFS] O. Fujino, T. Fujisawa, M. Saito, Some remarks on the semipositivity theorems, Publ. Res. Inst. Math. Sci. 50 (2014), no. 1, 85–112.

[FG] O. Fujino, Y. Gongyo, On canonical bundle formulas and subadjunctions, Michigan Math. J. 61 (2012), no. 2, 255–264.

[FLh1] O. Fujino, H. Liu, On normalization of quasi-log canonical pairs, Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 10, 97–101.

[FLh2] O. Fujino, H. Liu, Quasi-log canonical pairs are Du Bois, to appear in J. Algebraic Geom.

[FLh3] O. Fujino, H. Liu, Fujita-type freeness for quasi-log canonical curves and surfaces, to appear in Kyoto Journal of Mathematics.

[FLw] O. Fujino, W. Liu, Simple connectedness of Fano log pairs with semi-log canonical singularities, Math. Z. 295 (2020), no. 1-2, 341–348.

[Ka1] Y. Kawamata, On the length of an extremal rational curve, Invent. Math. 105 (1991), no. 3, 609–611.

[Ka2] Y. Kawamata, Subadjunction of log canonical divisors. II, Amer. J. Math. 120 (1998), no. 5, 893–899.

[Kl1] J. Koll´ar, Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Math- ematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 32. Springer-Verlag, Berlin, 1996.

[Kl2] J. Koll´ar, Singularities of the minimal model program. With a collaboration of S´andor Kov´acs, Cambridge Tracts in Mathematics, 200. Cambridge University Press, Cam- bridge, 2013.

[L] R. Lazarsfeld, Positivity in algebraic geometry. II. Positivity for vector bundles, and multiplier ideals, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 49. Springer-Verlag, Berlin, 2004.

[LZ] S. Lu, D.-Q. Zhang, Positivity criteria for log canonical divisors and hyperbolicity, J. Reine Angew. Math. 726 (2017), 173–186.

[S] R. Svaldi, Hyperbolicity for log canonical pairs and the cone theorem, Selecta Math. (N.S.) 25 (2019), no. 5, Art. 67, 23 pp.