Hi!


I fear that I am up to ask a very vague question, but more than an answer I need a suggestion of references I should look up.


I need to know everything about Tor sheaves and what do they tell about geometry. For example if $X$ is a smooth variety and $Z$ and $B$ are subvarieties,where are the sheaves $\mathbf{Tor}\_i(O\_Z, O\_B)$ supported? Does the vanishing of (some) of the higher Tor sheaves have some reflection on the mutual geometry of $Z$ and $B$ (for example can we evince the dimension of the intersection of $B$ and $Z$).


As I already explain you do not need to answer this (probably very silly) questions. I just need someone to point the right book to me, since right know I have not the slightest idea of where to find these informations. 


Thank you very much for your time and your attention,


Best



Tor sheaves: what do they tell us about geometry
$\text{Tor}(O\_Z, O\_B)$ certainly tells you about the intersection of $Z$ and $B$ and is supported on $Z \cap B$ (essentially by definition).


One common interpretation of these sheaves is in [intersection theory (on wikipedia)](http://en.wikipedia.org/wiki/Intersection_theory). In particular, they are used to compute the intersection number. See for example Chapter 20 of W. Fulton's book *Intersection Theory*. 


