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ADJUNCTION AND INVERSION OF ADJUNCTION

Part of: Projective and enumerative geometry Birational geometry

Published online by Cambridge University Press:  05 September 2022

OSAMU FUJINO Open the ORCID record for OSAMU FUJINO [Opens in a new window]  and
KENTA HASHIZUME Open the ORCID record for KENTA HASHIZUME [Opens in a new window]
OSAMU FUJINO
Affiliation:
Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan fujino@math.kyoto-u.ac.jp
KENTA HASHIZUME
Affiliation:
Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan hkenta@math.kyoto-u.ac.jp
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Abstract

We establish adjunction and inversion of adjunction for log canonical centers of arbitrary codimension in full generality.

Keywords

adjunctioninversion of adjunctionlog canonical centersgeneralized pairs

MSC classification

Primary: 14E30: Minimal model program (Mori theory, extremal rays)
Secondary: 14N30: Adjunction problems

Information

Type
Article
Information
Nagoya Mathematical Journal , Volume 249 , March 2023 , pp. 119 - 147
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Foundation Nagoya Mathematical Journal

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Footnotes

Fujino was partially supported by JSPS KAKENHI Grant Numbers JP16H03925, JP16H06337, JP19H01787, JP20H00111, and JP21H00974. Hashizume was partially supported by JSPS KAKENHI Grant Numbers JP16J05875 and JP19J00046.

References

Altman, A. and Kleiman, S., Introduction to Grothendieck Duality Theory, Lecture Notes in Math. 146, Springer, Berlin–New York, 1970.CrossRefGoogle Scholar
Bierstone, E. and Vera Pacheco, F., Resolution of singularities of pairs preserving semi-simple normal crossings , Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 107 (2013), 159–188.CrossRefGoogle Scholar
Filipazzi, S., On a generalized canonical bundle formula and generalized adjunction , Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 21 (2020), 1187–1221.Google Scholar
Fujino, O., Fundamental theorems for the log minimal model program , Publ. Res. Inst. Math. Sci. 47 (2011), 727–789.CrossRefGoogle Scholar
Fujino, O., Foundations of the Minimal Model Program, MSJ Memoirs 35, Math. Soc. Japan, Tokyo, 2017.CrossRefGoogle Scholar
Fujino, O., Fundamental properties of basic slc-trivial fibrations I , Publ. Res. Inst. Math. Sci. 58 (2022), 473–526.CrossRefGoogle Scholar
Fujino, O., Cone theorem and Mori hyperbolicity, preprint, arXiv:2102.11986 [math.AG]Google Scholar
Fujino, O. and Fujisawa, T., Variations of mixed Hodge structure and semipositivity theorems , Publ. Res. Inst. Math. Sci. 50 (2014), 589–661.CrossRefGoogle Scholar
Fujino, O., Fujisawa, T., and Liu, H., Fundamental properties of basic slc-trivial fibrations II , Publ. Res. Inst. Math. Sci. 58 (2022), 527–549.CrossRefGoogle Scholar
Fujino, O. and Hashizume, K., On inversion of adjunction , Proc. Japan Acad. Ser. A Math. Sci. 98 (2022), 13–18.CrossRefGoogle Scholar
Fujino, O. and Hashizume, K., Existence of log canonical modifications and its applications, preprint, arXiv:2103.01417 [math.AG]Google Scholar
Hacon, C. D., On the log canonical inversion of adjunction , Proc. Edinb. Math. Soc. (2) 57 (2014), 139–143.CrossRefGoogle Scholar
Han, J. and Li, Z., Weak Zariski decompositions and log terminal models for generalized polarized pairs , Math. Z. (2022), to appear.CrossRefGoogle Scholar
Hu, Z., Existence of canonical models for Kawamata log terminal pairs, preprint, arXiv:2004.03895 [math.AG]Google Scholar
Kawakita, M., Inversion of adjunction on log canonicity , Invent. Math. 167 (2007), 129–133.CrossRefGoogle Scholar
Kawamata, Y., “Subadjunction of log canonical divisors for a subvariety of codimension 2” in Birational Algebraic Geometry (Baltimore, MD, 1996), Contemp. Math. 207, Amer. Math. Soc., Providence, RI, 1997, 79–88.CrossRefGoogle Scholar
Prokhorov, Y. and Shokurov, V. V., Towards the second main theorem on complements , J. Algebraic Geom. 18 (2009), 151–199.CrossRefGoogle Scholar