On the moduli b-divisors of lc-trivial fibrations

Osamu Fujino[1]; Yoshinori Gongyo[2]

  • [1] Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan
  • [2] Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914 Japan. Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 4, page 1721-1735
  • ISSN: 0373-0956

Abstract

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Roughly speaking, by using the semi-stable minimal model program, we prove that the moduli part of an lc-trivial fibration coincides with that of a klt-trivial fibration induced by adjunction after taking a suitable generically finite cover. As an application, we obtain that the moduli part of an lc-trivial fibration is b-nef and abundant by Ambro’s result on klt-trivial fibrations.

How to cite

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Fujino, Osamu, and Gongyo, Yoshinori. "On the moduli b-divisors of lc-trivial fibrations." Annales de l’institut Fourier 64.4 (2014): 1721-1735. <http://eudml.org/doc/275511>.

@article{Fujino2014,
abstract = {Roughly speaking, by using the semi-stable minimal model program, we prove that the moduli part of an lc-trivial fibration coincides with that of a klt-trivial fibration induced by adjunction after taking a suitable generically finite cover. As an application, we obtain that the moduli part of an lc-trivial fibration is b-nef and abundant by Ambro’s result on klt-trivial fibrations.},
affiliation = {Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan; Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, 153-8914 Japan. Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK},
author = {Fujino, Osamu, Gongyo, Yoshinori},
journal = {Annales de l’institut Fourier},
keywords = {semi-stable minimal model program; canonical bundle formulae; lc-trivial fibrations; klt-trivial fibrations},
language = {eng},
number = {4},
pages = {1721-1735},
publisher = {Association des Annales de l’institut Fourier},
title = {On the moduli b-divisors of lc-trivial fibrations},
url = {http://eudml.org/doc/275511},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Fujino, Osamu
AU - Gongyo, Yoshinori
TI - On the moduli b-divisors of lc-trivial fibrations
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 4
SP - 1721
EP - 1735
AB - Roughly speaking, by using the semi-stable minimal model program, we prove that the moduli part of an lc-trivial fibration coincides with that of a klt-trivial fibration induced by adjunction after taking a suitable generically finite cover. As an application, we obtain that the moduli part of an lc-trivial fibration is b-nef and abundant by Ambro’s result on klt-trivial fibrations.
LA - eng
KW - semi-stable minimal model program; canonical bundle formulae; lc-trivial fibrations; klt-trivial fibrations
UR - http://eudml.org/doc/275511
ER -

References

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  1. F. Ambro, Shokurov’s boundary property, J. Differential Geom. 67 (2004), 229-255 Zbl1097.14029MR2153078
  2. F. Ambro, The moduli b-divisor of an lc-trivial fibration, Compos. Math. 141 (2005), 385-403 Zbl1094.14025MR2134273
  3. C. Birkar, Y. Chen, Images of manifolds with semi-ample anti-canonical divisor Zbl06560854
  4. A. Corti, 3 -fold flips after Shokurov, Flips for -folds and -folds 35 (2007), 18-48, Oxford Univ. Press, Oxford Zbl1286.14022MR2359340
  5. P. Deligne, Théorie de Hodge. II, (French) Inst. Hautes Études Sci. Publ. Math. 40 (1971), 5-57 Zbl0219.14007MR498551
  6. E. Floris, Inductive approach to effective b-semiampleness, Int. Math. Res. Not. IMRN 2014 (2014), 1645-1492 Zbl1325.14018MR3180598
  7. O. Fujino, Higher direct images of log canonical divisors and positivity theorems Zbl1072.14019
  8. O. Fujino, Abundance theorem for semi log canonical threefolds, Duke Math. J. 102 (2000), 513-532 Zbl0986.14007MR1756108
  9. O. Fujino, A canonical bundle formula for certain algebraic fiber spaces and its applications, Nagoya Math. J. 172 (2003), 129-171 Zbl1072.14040MR2019523
  10. O. Fujino, Higher direct images of log canonical divisors, J. Differential Geom. 66 (2004), 453-479 Zbl1072.14019MR2106473
  11. O. Fujino, What is log terminal?, Flips for -folds and -folds 35 (2007), 49-62, Oxford Univ. Press, Oxford Zbl1286.14024MR2359341
  12. O. Fujino, Fundamental theorems for the log minimal model program, Publ. Res. Inst. Math. Sci. 47 (2011), 727-789 Zbl1234.14013MR2832805
  13. O. Fujino, On Kawamata’s theorem, Classification of algebraic varieties (2011), 305-315, EMS Ser. Congr. Rep., Eur. Math. Soc., Zürich Zbl1213.14015MR2779478
  14. O. Fujino, Semi-stable minimal model program for varieties with trivial canonical divisor, Proc. Japan Acad. Ser. A Math. Sci. 87 (2011), 25-30 Zbl1230.14016MR2802603
  15. O. Fujino, Basepoint-free theorems: saturation, b-divisors, and canonical bundle formula, Algebra Number Theory 6 (2012), 797-823 Zbl1251.14005MR2966720
  16. O. Fujino, Some remarks on the minimal model program for log canonical pairs, (to appear in Kodaira Centennial issue of Journal of Mathematical Sciences, the University of Tokyo) 
  17. O. Fujino, T. Fujisawa, Variations of mixed Hodge structure and semi-positivity theorems Zbl1305.14004
  18. N. M. Katz, The regularity theorem in algebraic geometry, Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 1 (1971), 437-443, Gauthier-Villars, Paris Zbl0235.14006MR472822
  19. Y. Kawamata, Subadjunction of log canonical divisors for a subvariety of codimension 2 , Birational algebraic geometry (Baltimore, MD, 1996) (1997), 79-88, Amer. Math. Soc., Providence, RI Zbl0901.14004MR1462926
  20. G. Kempf, F. Knudsen, D. Mumford, Saint-Donat B., Toroidal embeddings. I, 339 (1973), Springer-Verlag, Berlin-New York Zbl0271.14017MR335518
  21. J. Kollár, Kodaira’s canonical bundle formula and adjunction, Flips for -folds and -folds 35 (2007), 134-162, Oxford Univ. Press, Oxford Zbl1286.14027MR2359346
  22. Yu. G. Prokhorov, V. V. Shokurov, Towards the second main theorem on complements, J. Algebraic Geom. 18 (2009), 151-199 Zbl1159.14020MR2448282
  23. M.-H. Saito, Y. Shimizu, S. Usui, Variation of mixed Hodge structure and the Torelli problem, Algebraic geometry, Sendai, 1985 (1987), 649-693, North-Holland, Amsterdam Zbl0643.14005MR946252

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