Reference on an equivariant resolution of singularities Let $X$ be an algebraic variety over $\mathbb{C}$ (or a normal complex space). 
I found the word "equivariant resolution" in several papers on singularity theory or deformation theory. I think that it means the birational proper morphism of complex spaces $f: Y \rightarrow X $ where $Y$ is a complex manifold such that $f_{\ast} \Theta_Y \simeq \Theta_X$ where $\Theta_X$ is the tangent sheaf, i.e. the dual of the Kahler differential sheaf on $X$ and $\Theta_Y$ is the tangent sheaf on $Y$. 
Question 1 Does that equivariant resolution always exist for an complex algebraic variety $X$? 
Question 2 Can $Y$ be taken as an smooth algebraic variety? 
If you know the reference, please let me know about it. In Wahl's paper on equisingular deformations, the preprint by Hironaka was cited but I couldn't find it.
 A: The word "equivariant" usually refers to doing whatever indicated by also respecting a group action. In the context of your question this means that there is a group action on $X$ and it is lifted to $Y$ such that $f$ is equivariant with respect to the lifted action.
A relevant reference is 
MR1453072 (98c:14011) 
Abramovich, Dan(1-BOST); Wang, Jianhua(1-MIT)
Equivariant resolution of singularities in characteristic 0. (English summary) 
Math. Res. Lett. 4 (1997), no. 2-3, 427–433. 
14E15 
A: Two other references:
Bierstone, Edward; Milman, Pierre D. (1997), "Canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant.", Invent. Math. 128 (2): 207–302, doi:10.1007/s002220050141, MR1440306
Encinas, S.; Villamayor, O. (1998), "Good points and constructive resolution of singularities.", Acta Math. 181 (1): 109–158, doi:10.1007/BF02392749, MR1654779
From what I understand, both references provide a canonical resolution in characteristic zero which is functorial for smooth morphisms (in particular equivariant, compatible with restriction to open subsets, etc.).
