RT Journal Article
T1 On `maximal' poles of zeta functions, roots of b-functions and monodromy jordan blocks
A1 Melle Hernández, Alejandro
A1 Torrelli, Tristan
A1 Veys, Willen
AB The main objects of this study are the poles of several local zeta functions: the Igusa, topological, and motivic zeta function associated to a polynomial or (germ of) holomorphic function in n variables. We are interested in poles of maximal possible order n. In all known cases (curves, non-degenerate polynomials) there is at most one pole of maximal order n, which is then given by the log canonical threshold of the function at the corresponding singular point. For an isolated singular point we prove that if the log canonical threshold yields a pole of order n of the corresponding (local) zeta function, then it induces a root of the Bernstein-Sato polynomial of the given function of multiplicity n, (proving one of the cases of the strongest form of a conjecture of Igusa-Denef-Loeser). For an arbitrary singular point, we show under the same assumption that the monodromy eigenvalue induced by the pole has 'a Jordan block of size n on the (perverse) complex of nearby cycles'.
PB Oxford Univ. Press.
SN 1753-8416
YR 2009
FD 2009
LK https://hdl.handle.net/20.500.14352/49745
UL https://hdl.handle.net/20.500.14352/49745
LA eng
NO MTM
NO Fund of Scientific Research-Flanders
DS Docta Complutense
RD 19 abr 2025