Asian Journal of Mathematics

Volume 21 (2017)

Number 3

Logarithmic version of the Milnor formula

Pages: 571 – 590

DOI: https://dx.doi.org/10.4310/AJM.2017.v21.n3.a8

Author

Enlin Yang (Department of Mathematical Sciences, Tsinghua University, Beijing, China; and Freie Universität, Berlin, Germany)

Abstract

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).

Keywords

Milnor formula, vanishing cycle, characteristic cycle

2010 Mathematics Subject Classification

14F20, 14G17

Received 20 July 2015

Published 5 July 2017