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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Towards the second main theorem on complements

Authors: Yu. G. Prokhorov and V. V. Shokurov
Journal: J. Algebraic Geom. 18 (2009), 151-199
Published electronically: April 24, 2008
MathSciNet review: 2448282
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Abstract | References | Additional Information

Abstract: We prove the boundedness of complements modulo two conjectures: Borisov–Alexeev conjecture and effective adjunction for fibre spaces. We discuss the last conjecture and prove it in two particular cases.

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Additional Information

Yu. G. Prokhorov
Affiliation: Department of Algebra, Faculty of Mathematics, Moscow State University, Moscow 117234, Russia

V. V. Shokurov
Affiliation: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
Address at time of publication: Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina str. 8, 119991, Moscow, Russia

Received by editor(s): November 5, 2006
Received by editor(s) in revised form: September 16, 2007
Published electronically: April 24, 2008
Additional Notes: The first author was partially supported by grants CRDF-RUM, No. 1-2692-MO-05 and RFBR, No. 05-01-00353-a, 06-01-72017. The second author was partially supported by NSF grant DMS-0400832.