Journal of Algebraic Geometry

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		Online ISSN 1534-7486; Print ISSN 1056-3911

On factoriality of nodal threefolds

Author(s): Ivan Cheltsov
Journal: J. Algebraic Geom. 14 (2005), 663-690.
Posted: May 11, 2005
MathSciNet review: 2147353
Retrieve article in: PDF

Abstract | References | Additional information

Abstract: We prove the $\mathbb{Q}$ -factoriality of a nodal hypersurface in $\mathbb{P} ^{4}$ of degree with at most ${\frac{(n-1)^{2}}{4}}$ nodes and the $\mathbb{Q}$ -factoriality of a double cover of $\mathbb{P} ^{3}$ branched over a nodal surface of degree with at most ${\frac{(2r-1)r}{3}}$ nodes.

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Additional Information:

Ivan Cheltsov
Affiliation: Steklov Institute of Mathematics, 8 Gubkin street, Moscow 117966, Russia
Address at time of publication: School of Mathematics, The University of Edinburgh, Kings Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK
Email: cheltsov@yahoo.com, I.Cheltsov@ed.ac.uk
DOI: 10.1090/S1056-3911-05-00405-4
PII: S 1056-3911(05)00405-4
Received by editor(s): June 17, 2004
Received by editor(s) in revised form: October 6, 2004, October 18, 2004, and November 21, 2004
Posted: May 11, 2005
Additional Notes: The author is very grateful to A. Corti, M. Grinenko, V. Iskovskikh, S. Kudryavtsev, V. Kulikov, M. Mella, J. Park, Yu. Prokhorov, A. Pukhlikov, V. Shokurov, L. Wotzlaw for fruitful conversations. Special thanks goes to V. Kulikov for Lemma 38. The author would also like to thank the referee for useful comments. \indent All varieties are assumed to be projective, normal, and defined over $\mathbb{C}$.

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