manuscripta mathematica

, Volume 104, Issue 3, pp 275–294 | Cite as

Hilbert–Kunz multiplicity, McKay correspondence and good ideals¶in two-dimensional rational singularities

  • Kei-ichi Watanabe
  • Ken-ichi Yoshida


Hilbert–Kunz multiplicity is known to be a very mysterious invariant of a ring or an ideal. We will show a very beautiful formula on Hilbert–Kunz multiplicity for integrally closed ideals in two-dimensional Gorenstein rational singularities. In the proof, “McKay correspondence” and “Riemann–Roch formula” play essential roles. Also this formula gives a new significance to “good ideals”.

Mathematics Subject Classification (2000): Primary 13D40; Secondary 13A35, 14C40, 14B05 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Kei-ichi Watanabe
    • 1
  • Ken-ichi Yoshida
    • 2
  1. 1.Department of Mathematics, College of Humanities and Sciences, Nihon University, Setagaya-ku, Tokyo, 1560045, Japan. e-mail:
  2. 2.Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 4648602, Japan. e-mail:

Personalised recommendations