Suppose I have a (2,4) complete intersection 3-fold $X\subset\mathbb P\_{\mathbb C}^5$ with 118 nodal ($A\_1$) singularities (if it simplifies things then assume it's the intersection of the Grassmanian $G(2,4)$ with a quartic). It is known (for example see Theorem 4.3 and Corollary 4.4 in Dimca's "Singularities and Topology of Hypersurfaces") that $H\_1(X,\mathbb Z)=H\_1(\mathbb P^3,\mathbb Z)=0$ and that $H\_4(X,\mathbb Z)$ is torsion free. 


Does anyone know if taking a crepant resolution $\tilde{X}$ of these 118 nodes could introduce torsion into $H\_1$ or $H\_4$ of the resolution? Specifically, does it introduce 2-torsion?



Effect of crepant resolution on the torsion in homology of a complete intersection 3-fold
If I am not mistaken, the mapping $\tilde X\to X$ blows down a disjoint union of 2-dimensional spheres, so it follows from the homology sequence of pair that it induces isomorphisms of both $H\_1$'s and $H\_4$'s (with integer coefficients). 


