Abstract
Deformation theory is an important aspect of the study about isolated singularities. The invariant called irregularity is very useful in the study on the deformation of isolated singularities. In this note we give an optimal upper bound for a class of surface singularities by the computation of cohomology. Moreover a sufficient condition is given for the positivity of irregularity of some simple hyperbolic surface singularities. Therefore a class of surface singularities with non-rigid deformation is constructed.
Similar content being viewed by others
References
Arbarello, E., Cornalba, M., Griffiths, P.A. & Harris, J., Geometry of algebraic curves, Vol. 1, Springer-Verlag, 1985.
Laufer, H., Normal two-dimensional singularities, Annals of Mathematics studies 71, Princeton Univ. Press.
Pinkham, H., Singularités rationnelle de surfaces, Appendice, Séminarire sur les singularités des surfaces, Springer-Verlag, Lect. Notes in Math.,777, 147–178.
Stephen S-T Yau,s (n−1) invariant for isolated n-dimensional singularities and its application to modulo problem, Amer. J. Math.,104 (1982), 829–841.
Stephen S-T Yau,Various numerical invariants for isolated singularities, Amer. J. Math.,104 (1982), 1063–1100.
Wahl, J.,Deformation of quasihomogeneous surface singularities, Math. Ann.,1 (1988), 105–128.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hao, C. A note on irregularity of two dimensional simple hyperbolic singularities. Acta Mathematica Sinica 10, 396–400 (1994). https://doi.org/10.1007/BF02582035
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02582035