Asian Journal of Mathematics
Volume 21 (2017)
Logarithmic version of the Milnor formula
Pages: 571 – 590
In this paper, we propose a logarithmic version of the Milnor formula. It is a formula for the total dimension of vanishing cycles with tamely ramified coefficient sheaves at an isolated log-singular point. We prove this formula in the geometric case. In the geometric case, it implies that the total dimension of vanishing cycles with tamely ramified coefficient sheaves can be computed as an intersection number (in terms of characteristic cycle).
Milnor formula, vanishing cycle, characteristic cycle
2010 Mathematics Subject Classification
Paper received on 20 July 2015.