Betti numbers of hypersurfaces and defects of linear systems
Alexandru Dimca
Source: Duke Math. J. Volume 60, Number 1 (1990), 285-298.
First Page PDF: View first page of article (PDF, 102 KB)Primary Subjects: 14J70
Secondary Subjects: 14C30, 14F25, 32S50
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077297148
Mathematical Reviews number (MathSciNet):
MR1047124
Zentralblatt MATH identifier:
0729.14017
Digital Object Identifier: doi:10.1215/S0012-7094-90-06010-7
References
[1] D. Burghelea and A. Verona, Local homological properties of analytic sets, Manuscripta Math. 7 (1972), 55–66.
Mathematical Reviews (MathSciNet):
MR46:9386
Zentralblatt MATH:
0246.32007
Digital Object Identifier: doi:10.1007/BF01303536
[2] C. H. Clemens, Double Solids, Adv. in Math. 47 (1983), no. 2, 107–230.
Mathematical Reviews (MathSciNet):
MR85e:14058
Zentralblatt MATH:
0509.14045
Digital Object Identifier: doi:10.1016/0001-8708(83)90025-7
[3]1 P. Deligne, Théorie de Hodge II, Inst. Hautes Études Sci. Publ. Math. (1971), no. 40, 5–57.
Mathematical Reviews (MathSciNet):
MR58:16653a
Zentralblatt MATH:
0219.14007
Digital Object Identifier: doi:10.1007/BF02684692
[3]2 P. Deligne, Théorie de Hodge III, Inst. Hautes Études Sci. Publ. Math. (1974), no. 44, 5–77.
Mathematical Reviews (MathSciNet):
MR58:16653b
Zentralblatt MATH:
0237.14003
Digital Object Identifier: doi:10.1007/BF02685881
[4] A. Dimca, On the homology and cohomology of complete intersections with isolated singularities, Compositio Math. 58 (1986), no. 3, 321–339.
Mathematical Reviews (MathSciNet):
MR87m:14022
Zentralblatt MATH:
0598.14017
[5] A. Dimca, Topics on Real and Complex Singularities, Advanced Lectures in Mathematics, Vieweg, Braunschweig-Wiesbaden, 1987.
Mathematical Reviews (MathSciNet):
MR92d:32048
Zentralblatt MATH:
0628.14001
[6] A. Dimca, On the Milnor fibrations of weighted homogeneous polynomials, Compositio Math. (to appear).
Mathematical Reviews (MathSciNet):
MR1078856
[7] A. Dimca and S. Dimiev, On analytic coverings of weighted projective spaces, Bull. London Math. Soc. 17 (1985), no. 3, 234–238.
Mathematical Reviews (MathSciNet):
MR87b:32015
Zentralblatt MATH:
0546.14006
Digital Object Identifier: doi:10.1112/blms/17.3.234
[8] I. Dolgachev, Weighted projective varieties, Group Actions and Vector Fields (Vancouver, B.C., 1981) ed. J. B. Carrell, Lecture Notes in Math., vol. 956, Springer, Berlin, 1982, pp. 34–71.
Mathematical Reviews (MathSciNet):
MR85g:14060
Zentralblatt MATH:
0516.14014
Digital Object Identifier: doi:10.1007/BFb0101508
[9] A. H. Durfee, Fifteen characterizations of rational double points and simple critical points, Enseign. Math. (2) 25 (1979), no. 1-2, 131–163.
Mathematical Reviews (MathSciNet):
MR80m:14003
Zentralblatt MATH:
0418.14020
[10] A. H. Durfee, Mixed Hodge structures on punctured neighborhoods, Duke Math. J. 50 (1983), no. 4, 1017–1040.
Mathematical Reviews (MathSciNet):
MR85m:14012
Zentralblatt MATH:
0545.14005
Digital Object Identifier: doi:10.1215/S0012-7094-83-05043-3
Project Euclid: euclid.dmj/1077303488
[11] W. Ebeling, Quadratische Formen und Monodromiegruppen von Singularitäten, Math. Ann. 255 (1981), no. 4, 463–498.
Mathematical Reviews (MathSciNet):
MR82j:14003
Zentralblatt MATH:
0438.32004
Digital Object Identifier: doi:10.1007/BF01451928
[12] H. Esnault, Fibre de Milnor d'un cône sur une courbe plane singulière, Invent. Math. 68 (1982), no. 3, 477–496.
Mathematical Reviews (MathSciNet):
MR84a:14003
Zentralblatt MATH:
0475.14018
Digital Object Identifier: doi:10.1007/BF01389413
[13] P. Griffiths, On the periods of certain rational integrals. I, II, Ann. of Math. (2) 90 (1969), 460-495; ibid. (2) 90 (1969), 496–541.
Mathematical Reviews (MathSciNet):
MR41:5357
Zentralblatt MATH:
0215.08103
Digital Object Identifier: doi:10.2307/1970747
JSTOR: links.jstor.org
[14] A. Grothendieck, On the de Rham cohomology of algebraic varieties, Inst. Hautes Études Sci. Publ. Math. (1966), no. 29, 95–103.
Mathematical Reviews (MathSciNet):
MR33:7343
Zentralblatt MATH:
0145.17602
Digital Object Identifier: doi:10.1007/BF02684807
[15] M. Reid, Young person's guide to canonical singularities, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Proc. Symp. Pure Math., Part 1, vol. 46, Amer. Math. Soc., Providence, RI, 1987, Proc. AMS Summer Institute Bowdoin, pp. 345–414.
Mathematical Reviews (MathSciNet):
MR89b:14016
Zentralblatt MATH:
0634.14003
[16] K. Saito, Einfach-elliptische Singularitäten, Invent. Math. 23 (1974), 289–325.
Mathematical Reviews (MathSciNet):
MR50:7147
Zentralblatt MATH:
0296.14019
Digital Object Identifier: doi:10.1007/BF01389749
[17] C. Schoen, Algebraic cycles on certain desingularized nodal hypersurfaces, Math. Ann. 270 (1985), no. 1, 17–27.
Mathematical Reviews (MathSciNet):
MR86d:14010
Zentralblatt MATH:
0533.14002
Digital Object Identifier: doi:10.1007/BF01455524
[18] D. Siersma, Quasihomogeneous singularities with transversal type $A_ 1$, Singularities (Iowa City, IA, 1986), Contemp. Math., vol. 90, Amer. Math. Soc., Providence, RI, 1989, pp. 261–294.
Mathematical Reviews (MathSciNet):
MR91a:32050
Zentralblatt MATH:
0682.32012
[19] J. H. M. Steenbrink, Intersection form for quasi-homogeneous singularities, Compositio Math. 34 (1977), no. 2, 211–223.
Mathematical Reviews (MathSciNet):
MR56:11995
Zentralblatt MATH:
0347.14001
[20] J. H. M. Steenbrink, Mixed Hodge structures associated with isolated singularities, Singularities, Part 2 (Arcata, Calif., 1981), Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, RI, 1983, pp. 513–536.
Mathematical Reviews (MathSciNet):
MR85d:32044
Zentralblatt MATH:
0515.14003
[21] J. H. M. Steenbrink, Mixed Hodge Structures and Singularities, book to appear.
[22] D. van Straten, On the Betti numbers of the Milnor fibre of a certain class of hypersurface singularities, Singularities, Representation of Algebras, and Vector Bundles (Lambrecht, 1985) eds. G.-M. Greuel and G. Trautmann, Lecture Notes in Math., vol. 1273, Springer, Berlin, 1987, pp. 203–220.
Mathematical Reviews (MathSciNet):
MR89d:32018
Zentralblatt MATH:
0638.14001
Digital Object Identifier: doi:10.1007/BFb0078845
[23] H. Terao, Forms with logarithmic pole and the filtration by the order of the pole, Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977), Kinokuniya Book Store, Tokyo, 1978, pp. 673–685.
Mathematical Reviews (MathSciNet):
MR82b:14004
Zentralblatt MATH:
0429.32015
[24] J. Werner, Kleine Auflösungen spezieller dreidimensionaler Varietäten, Bonner Mathematische Schriften [Bonn Mathematical Publications], 186, Universität Bonn Mathematisches Institut, Bonn, 1987.
Mathematical Reviews (MathSciNet):
MR89k:14018
Zentralblatt MATH:
0657.14021
[25] O. Zariski, On the problem of existence of algebraic functions of two variables possessing a given branch curve, Amer. J. Math. 51 (1929), 305–328.
Zentralblatt MATH:
55.0806.01
Mathematical Reviews (MathSciNet):
MR1506719
Digital Object Identifier: doi:10.2307/2370712
JSTOR: links.jstor.org
Duke Mathematical Journal