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.
On définit les invariants de Du Bois pour les singularités isolées d’espaces complexes. On établit leur relation avec les nombres de Hodge des groupes de cohomologie locale et évanescente. Nos résultats principaux relient le nombre de Tjurina de certaines singularités de Gorenstein avec les invariants de Du Bois et les nombres de Hodge du bord de la singularité, et expriment les nombres de Hodge de la fibre de Milnor de certaines intersections complètes de dimension trois en des termes similaires. On discute aussi la semicontinuité des invariants de du Bois sous déformation de la singularité.
@article{AIF_1997__47_5_1367_0, author = {Steenbrink, Joseph H. M.}, title = {Du {Bois} invariants of isolated complete intersection singularities}, journal = {Annales de l'Institut Fourier}, pages = {1367--1377}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {47}, number = {5}, year = {1997}, doi = {10.5802/aif.1603}, mrnumber = {99f:32058}, zbl = {0889.32035}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1603/} }
TY - JOUR AU - Steenbrink, Joseph H. M. TI - Du Bois invariants of isolated complete intersection singularities JO - Annales de l'Institut Fourier PY - 1997 SP - 1367 EP - 1377 VL - 47 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1603/ DO - 10.5802/aif.1603 LA - en ID - AIF_1997__47_5_1367_0 ER -
%0 Journal Article %A Steenbrink, Joseph H. M. %T Du Bois invariants of isolated complete intersection singularities %J Annales de l'Institut Fourier %D 1997 %P 1367-1377 %V 47 %N 5 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1603/ %R 10.5802/aif.1603 %G en %F AIF_1997__47_5_1367_0
Steenbrink, Joseph H. M. Du Bois invariants of isolated complete intersection singularities. Annales de l'Institut Fourier, Volume 47 (1997) no. 5, pp. 1367-1377. doi : 10.5802/aif.1603. http://www.numdam.org/articles/10.5802/aif.1603/
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