Codimension Two Determinantal Varieties with Isolated Singularities
Abstract
We study codimension two determinantal varieties with isolated singularities. These singularities admit a unique smoothing, thus we can define their Milnor number as the middle Betti number of their generic fiber. For surfaces in C^4, we obtain a L\^e-Greuel formula expressing the Milnor number of the surface in terms of the second polar multiplicity and the Milnor number of a generic section. We also relate the Milnor number with Ebeling and Gusein-Zade index of the 1- form given by the differential of a generic linear projection defined on the surface. To illustrate the results, in the last section we compute the Milnor number of some normal forms from A. Fr\"uhbis-Kr\"uger and A. Neumer [2] list of simple determinantal surface singularities.
Cite
@article{arxiv.1110.5580,
title = {Codimension Two Determinantal Varieties with Isolated Singularities},
author = {Miriam da Silva Pereira and Maria Aparecida Soares Ruas},
journal= {arXiv preprint arXiv:1110.5580},
year = {2011}
}