Koszul complexes and hypersurface singularities

Choudary, A. D. R.; Dimca, A.

doi:10.1090/S0002-9939-1994-1189539-9

Koszul complexes and hypersurface singularities
HTML articles powered by AMS MathViewer

by A. D. R. Choudary and A. Dimca

Proc. Amer. Math. Soc. 121 (1994), 1009-1016

DOI: https://doi.org/10.1090/S0002-9939-1994-1189539-9

PDF | Request permission

Abstract:

The behavior of Poincaré series and Betti numbers of complex projective hypersurfaces in terms of their singularities is compared.

References

Alexandru Dimca, Topics on real and complex singularities, Advanced Lectures in Mathematics, Friedr. Vieweg & Sohn, Braunschweig, 1987. An introduction. MR 1013785, DOI 10.1007/978-3-663-13903-4
Alexandru Dimca, Betti numbers of hypersurfaces and defects of linear systems, Duke Math. J. 60 (1990), no. 1, 285–298. MR 1047124, DOI 10.1215/S0012-7094-90-06010-7
Alexandru Dimca, On the Milnor fibrations of weighted homogeneous polynomials, Compositio Math. 76 (1990), no. 1-2, 19–47. Algebraic geometry (Berlin, 1988). MR 1078856
Alexandru Dimca, Singularities and topology of hypersurfaces, Universitext, Springer-Verlag, New York, 1992. MR 1194180, DOI 10.1007/978-1-4612-4404-2
G.-M. Greuel, Der Gauss-Manin-Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten, Math. Ann. 214 (1975), 235–266. MR 396554, DOI 10.1007/BF01352108
Phillip A. Griffiths, On the periods of certain rational integrals. I, II, Ann. of Math. (2) 90 (1969), 460–495; 90 (1969), 496–541. MR 0260733, DOI 10.2307/1970746
Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
Hideyuki Matsumura, Commutative algebra, W. A. Benjamin, Inc., New York, 1970. MR 0266911
Gerardus Rudolf Pellikaan, Hypersurface singularities and resolutions of Jacobi modules, Drukkerij Elinkwijk B. V., Utrecht, 1985. Dissertation, Rijksuniversiteit te Utrecht, Utrecht, 1985; With a Dutch summary. MR 816348
Kyoji Saito, On a generalization of de-Rham lemma, Ann. Inst. Fourier (Grenoble) 26 (1976), no. 2, vii, 165–170 (English, with French summary). MR 413155
Dirk 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. MR 1000607, DOI 10.1090/conm/090/1000607
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) Lecture Notes in Math., vol. 1273, Springer, Berlin, 1987, pp. 203–220. MR 915176, DOI 10.1007/BFb0078845
B. Teissier, Introduction to equisingularity problems, Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974) Amer. Math. Soc., Providence, R.I., 1975, pp. 593–632. MR 0422256