@article{Ruas_Pereira_2014, title={Codimension Two Determinantal Varieties with Isolated Singularities}, volume={115}, url={https://www.mscand.dk/article/view/19220}, DOI={10.7146/math.scand.a-19220}, abstractNote={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 $\mathsf{C}^4$, we obtain a Lê-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 Frühbis-Krüger and Neumer [7] list of simple determinantal surface singularities. }, number={2}, journal={MATHEMATICA SCANDINAVICA}, author={Ruas, Maria Aparecida Soares and Pereira, Miriam Da Silva}, year={2014}, month={Dec.}, pages={161–172} }