Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

On factoriality of nodal threefolds


Author: Ivan Cheltsov
Journal: J. Algebraic Geom. 14 (2005), 663-690
DOI: https://doi.org/10.1090/S1056-3911-05-00405-4
Published electronically: May 11, 2005
MathSciNet review: 2147353
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Abstract | References | Additional Information

Abstract: We prove the $\mathbb{Q} $-factoriality of a nodal hypersurface in $\mathbb{P} ^{4}$ of degree $n$ 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 $2r$ 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: https://doi.org/10.1090/S1056-3911-05-00405-4
Received by editor(s): June 17, 2004
Received by editor(s) in revised form: October 6, 2004, October 18, 2004, and November 21, 2004
Published electronically: 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 \ref{lemma:double-solid-III}. 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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