most recent 30 from http://mathoverflow.net 2013-05-20T13:20:38Z http://mathoverflow.net/feeds/question/47720 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/47720/monodromy-of-plane-curve-singularities David Marín 2010-11-29T20:55:28Z 2010-11-30T08:59:53Z

<p>Are there two IRREDUCIBLE plane curve singularities having different equisingular type with the same monodromy (linear action on the first homology group of the (regular) Milnor fibre)?</p>

http://mathoverflow.net/questions/47720/monodromy-of-plane-curve-singularities/47768#47768 Vivek Shende 2010-11-30T08:59:53Z 2010-11-30T08:59:53Z

<p>No, it is a classical theorem of Zariski that the Alexander polynomial, i.e., the characteristic polynomial of the monodromy of the Milnor fibre, determines the equisingularity class in these cases. </p> <p>In fact, from <a href="http://arxiv.org/abs/math/0205111" rel="nofollow">the theorem of Campillo, Delgado, and Gusein-Zade</a>, one sees that the zeta function of the monodromy -- i.e., the Alexander polynomial divided by $(1-t)$ -- is the Poincaré series of the semigroup of the curve singularity. </p>