Graduate Seminar
The monodromy conjecture for nondegenerate surface singularities.
Ann Lemahieu (Paris)
13 Dec 2009, 15:15
FU-Berlin
Inst. f. Mathematik
Arnimallee 3, Rm. 119
The monodromy conjecture predicts a relation between the geometry and the topology of a singularity. In particular, it says that a pole s_0 of the local topological zeta function in 0 induces an eigenvalue of monodromy e^2i pi s_0 at a point in the neighbourhood of 0. When the singularity is given by a polynomial that is nondegenerate with respect to its Newton polyhedron, then one can express the local topological zeta function and the zeta function of monodromy in terms of the Newton polyhedron. We analyze these formulas for surface singularities: we provide a set of monodromy eigenvalues and a set of false candidate poles. In this way we obtain a proof for the monodromy conjecture for nondegenerate surface singularities.
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