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Factorial threefold hypersurfaces
Author(s):
Ivan
Cheltsov
Journal:
J. Algebraic Geom.
Posted:
June 17, 2009
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References |
Additional information
Abstract:
Let be a hypersurface in of degree that has at worst isolated ordinary double points. We prove that is factorial in the case when has at most singular points.
References:
-
- 1.
- A. Andreotti, P. Salmon, Anelli con unica decomponibilita in fattori primi, ed un problema di intersezioni complete, Monatshefte für Mathematik 61 (1957), 97-142. MR 0104662 (21:3415)
- 2.
- E. Bese, On the spannedness and very ampleness of certain line bundles on the blow-ups of
and , Mathematische Annalen 262 (1983), 225-238. MR 690197 (84g:14006) - 3.
- I. Cheltsov, On factoriality of nodal threefolds, Journal of Algebraic Geometry 14 (2005), 663-690. MR 2147353 (2006k:14063)
- 4.
- I. Cheltsov, Non-rational nodal quartic threefolds, Pacific Journal of Mathematics 226 (2006), 65-82. MR 2247856 (2007e:14024)
- 5.
- I. Cheltsov, Points in projective spaces and application, Journal of Differential Geometry 81 (2009), 575-599. MR 2487601
- 6.
- I. Cheltsov, J. Park, Factorial hypersurfaces in
with nodes, Geometriae Dedicata 121 (2006), 205-219. MR 2276244 (2007m:14064) - 7.
- C. Ciliberto, V. Di Gennaro, Factoriality of certain hypersurfaces of
with ordinary double points, Encyclopaedia of Mathematical Sciences 132 (2004), 1-9. - 8.
- E. Davis, A. Geramita, F. Orecchia, Gorenstein algebras and the Cayley-Bacharach theorem, Proceedings of the American Mathematical Society 93 (1985), 593-597. MR 776185 (86k:14034)
- 9.
- E. Davis, A. Geramita, Birational morphisms to
: an ideal-theoretic perspective, Mathematische Annalen 279 (1988), 435-448. MR 922427 (89a:14014) - 10.
- A. Dimca, Betti numbers of hypersufaces and defects of linear systems, Duke Mathematical Journal 60 (1990), 285-298. MR 1047124 (91f:14041)
- 11.
- D. Eisenbud, M. Green, J. Harris, Cayley-Bacharach theorems and conjectures, Bulletin of the American Mathematical Society 33 (1996), 295-324. MR 1376653 (97a:14059)
- 12.
- D. Eisenbud, J-H. Koh, Remarks on points in a projective space, MSRI Publications 15, Springer, New York, 157-172. MR 1015517 (90i:14008)
- 13.
- R. Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Mathematics 156, Springer-Verlag (1970). MR 0282977 (44:211)
- 14.
- D. Kosta, Factoriality condition of some nodal threefolds in
, Manuscripta Mathematica 127 (2008), 151-166. MR 2442893 - 15.
- M. Mella, Birational geometry of quartic 3-folds II: the importance of being
-factorial, Mathematische Annalen 330 (2004), 107-126. MR 2091681 (2005h:14030)
Additional Information:
Ivan
Cheltsov
Affiliation:
School of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
Email:
i.cheltsov@ed.ac.uk
PII:
S 1056-3911(09)00522-0
Received by editor(s):
April 30, 2008
Received by editor(s) in revised form:
September 6, 2008
Posted:
June 17, 2009
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