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An inductive approach to generalized abundance using nef reduction
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 417-421.

We use the canonical bundle formula for parabolic fibrations to give an inductive approach to the generalized abundance conjecture using nef reduction. In particular, we observe that generalized abundance holds for a klt pair (X,B) if the nef dimension n(K X +B+L)=2 and K X +B0 or n(K X +B+L)=3 and κ(K X +B)>0.

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DOI : 10.5802/crmath.420

Priyankur Chaudhuri 1

1 Department of Mathematics, University of Maryland, College Park, MD 20742, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Priyankur Chaudhuri. An inductive approach to generalized abundance using nef reduction. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 417-421. doi : 10.5802/crmath.420. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.420/

[1] Florin Ambro The nef dimension of log minimal models (2004) (https://arxiv.org/abs/math/0411471)

[2] Florin Ambro Shokurov’s Boundary property, J. Differ. Geom., Volume 67 (2004) no. 2, pp. 229-255 | MR | Zbl

[3] Florin Ambro The moduli b-divisor of an lc-trivial fibration, Compos. Math., Volume 141 (2005) no. 2, pp. 385-403 | DOI | MR | Zbl

[4] Thomas Bauer; Frédéric Campana; Thomas Eckl; Stefan Kebekus; Thomas Peternell; Sławomir Rams; Tomasz Szemberg; Lorenz Wotzlaw A reduction map for nef line bundles, Complex geometry (Göttingen, 2000), Springer, 2002, pp. 27-36 | DOI | Zbl

[5] Osamu Fujino; Shigefumi Mori A canonical bundle formula, J. Differ. Geom., Volume 56 (2000) no. 1, pp. 167-188 | MR | Zbl

[6] Yoshinori Gongyo; Brian Lehmann Reduction maps and minimal model theory, Compos. Math., Volume 149 (2013) no. 2, pp. 295-308 | DOI | MR | Zbl

[7] Yujirp Kawamata; Katsumi Matsuda; Kenji Matsuki Introduction to the minimal model problem, Algebraic geometry, Sendai, 1985 (Advanced Studies in Pure Mathematics), Volume 10, North-Holland, 1987, pp. 283-360 | DOI | MR | Zbl

[8] János Kollár; Shigefumi Mori Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, 134, Cambridge University Press, 1998 (with the collaboration of C. H. Clemens and A. Corti. Translated from the 1998 Japanese original. ISBN: 0-521-63277-3) | DOI | Zbl

[9] Vladimir Lazić; Enrica Floris A travel guide to the canonical bundle formula, Birational Geometry and Moduli Spaces (Springer INdAM Series), Volume 39, Springer, 2020, pp. 37-55 | MR | Zbl

[10] Vladimir Lazić; Thomas Peternell On Generalised Abundance, I, Publ. Res. Inst. Math. Sci., Volume 56 (2020) no. 2, pp. 353-389 | DOI | MR | Zbl

[11] Vladimir Lazić; Thomas Peternell On Generalised Abundance, II, Peking Math. J., Volume 3 (2020) no. 1, pp. 1-46 | DOI | MR | Zbl

[12] Noboru Nakayama Zariski-decomposition and abundance, MSJ Memoirs, 14, Mathematical Society of Japan, 2004 | Numdam | Zbl

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