It is an apparently well known result that if one has a 1-parameter family of smooth Calabi-Yau 3-folds which acquires a node at a boundary point, then there is a vanishing lagrangian 3-sphere, and the geometrical monodromy is a Dehn-twist along this sphere whose effect on the homology of our base fiber is given by the classical Picard-Lefschetz formula $$\alpha \mapsto \alpha-(\delta\cdot \alpha) \delta,$$ where $\delta$ is the homology class of the vanishing 3-sphere. (This formula or an analogue of it actually holds in much more general families than just CY 3-folds, but that's the case I'm interested in). For a modern reference for the above result, see Chapter 3 of Looijenga's $\textit{Isolated Singular Points on Complete Intersections}$. 


My question is whether there is a known analogue for the case when the family in question acquires more than one $A\_1$-singularity. For example, if the smooth family acquires 4 nodes, is there a known formula for the monodromy action around such a fiber for Calabi-Yau 3-folds?


If no formula exists, is there any sense for what it's matrix might look like, roughly? Do we know, for example, that $Rank(S-1)=1$, where $S$ is the monodromy action and $1$ is the identity matrix?



Analogue of Picard-Lefschetz formulas for more than one node?
In general, I think that the monodromy should be
$$\alpha\mapsto \alpha - \sum\_i (\delta\_i\cdot \alpha)\delta\_i $$
where $\delta\_i$ are the vanishing cycles corresponding to each node. I'll see whether I can 
write down an outline of an argument later.


... Meanwhile later... Let me complement Tim's excellent comment with a more obscure explanation. The so called variation map $S-I: H^i(X\_t)\to H^i(X\_t)$ of the cohomology of the nearby fibre factors through a the cohomology of a (complex of) sheaf(ves) $\mathbb{R}\phi\mathbb{Z}$ supported on singular locus of the special fibre $X\_0$. In the case that $X\_0$ has isolated singularities, this sheaf decomposes into a sum of the corresponding sheaves supported at each of the critical points, and maps decomposes as well. The formula
I stated above would follow this together with the standard Picard-Lefschetz formula.


