We establish the rationality of simple isolated Cohen–Macaulay codimension (ICMC2) singularities in all dimensions and explicitly compute the vanishing homology of a certain class of threefolds including all the simple ones. ICMC2 singularities are determinantal and can be viewed as a natural generalization of complete intersections. The main tool for our investigations is the so-called Tjurina transformation—a special blowup construction based on the determinantal structure and often compatible with deformations.
"On the vanishing topology of isolated Cohen–Macaulay codimension singularities." Geom. Topol. 25 (5) 2167 - 2194, 2021. https://doi.org/10.2140/gt.2021.25.2167