Du Bois invariants of isolated complete intersection singularities

Joseph H. M. Steenbrink

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 5, page 1367-1377
  • ISSN: 0373-0956

Abstract

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We define Du Bois invariants for isolated singularities of complex spaces. We relate them to the Hodge numbers of the local and vanishing cohomology groups. Our main results express the Tjurina number of certain Gorenstein singularities in terms of Du Bois invariants and Hodge numbers of the link, and express the Hodge numbers of the Milnor fibre of certain three-dimensional complete intersections in similar terms. We also address the question of the semicontinuity of the Du Bois invariants under deformation of the singularity.

How to cite

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Steenbrink, Joseph H. M.. "Du Bois invariants of isolated complete intersection singularities." Annales de l'institut Fourier 47.5 (1997): 1367-1377. <http://eudml.org/doc/75267>.

@article{Steenbrink1997,
abstract = {We define Du Bois invariants for isolated singularities of complex spaces. We relate them to the Hodge numbers of the local and vanishing cohomology groups. Our main results express the Tjurina number of certain Gorenstein singularities in terms of Du Bois invariants and Hodge numbers of the link, and express the Hodge numbers of the Milnor fibre of certain three-dimensional complete intersections in similar terms. We also address the question of the semicontinuity of the Du Bois invariants under deformation of the singularity.},
author = {Steenbrink, Joseph H. M.},
journal = {Annales de l'institut Fourier},
keywords = {isolated complete intersection; Du Bois invariants; Hodge numbers},
language = {eng},
number = {5},
pages = {1367-1377},
publisher = {Association des Annales de l'Institut Fourier},
title = {Du Bois invariants of isolated complete intersection singularities},
url = {http://eudml.org/doc/75267},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Steenbrink, Joseph H. M.
TI - Du Bois invariants of isolated complete intersection singularities
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 5
SP - 1367
EP - 1377
AB - We define Du Bois invariants for isolated singularities of complex spaces. We relate them to the Hodge numbers of the local and vanishing cohomology groups. Our main results express the Tjurina number of certain Gorenstein singularities in terms of Du Bois invariants and Hodge numbers of the link, and express the Hodge numbers of the Milnor fibre of certain three-dimensional complete intersections in similar terms. We also address the question of the semicontinuity of the Du Bois invariants under deformation of the singularity.
LA - eng
KW - isolated complete intersection; Du Bois invariants; Hodge numbers
UR - http://eudml.org/doc/75267
ER -

References

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  1. [1] Ph. DU BOIS, Complexe de de Rham filtré d'une variété singulière, Bull. Soc. Math. France, 109 (1981), 41-81. Zbl0465.14009
  2. [2] G-M. GREUEL, Dualität in der lokalen Kohomologie isolierter Singularitäten, Math. Ann., 250 (1980), 157-173. Zbl0417.14003MR82e:32009
  3. [3] G.-M. GREUEL und LÊ DŭNG TRÀNG, Spitzen, Doppelpunkte und vertikale Tangenten in der Diskriminante verseller Deformationen von vollständigen Durchschnitten, Math. Ann., 222 (1976), 71-88. Zbl0318.32015
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  5. [5] F. GUILLÉN, V. NAVARRO AZNAR, P. PASCUAL-GAINZA, F. PUERTA, Hyperrésolutions cubiques et descente cohomologique, Lecture Notes in Math. 1335, Springer-Verlag, Berlin etc., 1988. Zbl0638.00011
  6. [6] S. ISHII, On isolated Gorenstein singularities, Math. Ann., 270 (1985), 541-554. Zbl0541.14002MR86j:32024
  7. [7] S. ISHII, Small deformations of normal singularities, Math. Ann., 275 (1986), 139-148. Zbl0586.14001MR87i:14003
  8. [8] E.J.N. LOOIJENGA, J.H.M. STEENBRINK, Milnor number and Tjurina number for complete intersections, Math. Ann., 251 (1985), 121-124. Zbl0539.14002
  9. [9] Y. NAMIKAWA, Deformation theory of Calabi-Yau threefolds and certain invariants of singularities, Preprint November 1995. 
  10. [10] Y. NAMIKAWA, J.H.M. STEENBRINK, Global smoothing of Calabi-Yau threefolds, Invent. Math., 122 (1995), 403-419. Zbl0861.14036MR96m:14056
  11. [11] J.H.M. STEENBRINK, Mixed Hodge structures associated with isolated singularities, Proc. Symp. Pure Math., 40, Part 2 (1983), 513-536. Zbl0515.14003MR85d:32044
  12. [12] J.H.M. STEENBRINK, Semicontinuity of the singularity spectrum, Invent. Math., 79 (1985), 557-565. Zbl0568.14021MR86h:32033
  13. [13] J.H.M. STEENBRINK, Vanishing theorems on singular spaces, Astérisque, 130 (1985), 330-341. Zbl0582.32039MR87j:14026
  14. [14] D. VAN STRATEN, J. STEENBRINK, Extendability of holomorphic differential forms near isolated hypersurface singularities, Abh. Math. Sem. Univ. Hamburg, 55 (1985), 97-110. Zbl0584.32018MR87j:32025
  15. [15] J.M. WAHL, A characterization of quasi-homogeneous Gorenstein surface singularities, Compos. Math., 55 (1985), 269-288. Zbl0587.14024MR87e:32013

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