Let $\mathcal{M}$ be a holonomic D-module on a complex analytic (or alternatively, algebraic) manifold $X$. One can attach to it (using a good filtration) a characteristic cycle $Ch(\mathcal{M})$ which is an analytic cycle on $T^\*X$ whose components are conic Lagrangian subvarieties and their multiplicities are positive integers (see e. g. Def. 1.8.5 in the book “Analytic D-modules and applications” by Bjoern). 



> 
> Is it true that for any short exact sequence of holonomic D-modules 
>  $$0\to \mathcal{M}\_1\to \mathcal{M}\_2\to \mathcal{M}\_3\to 0$$
>  one has 
>  $$Ch(\mathcal{M}\_2)=Ch(\mathcal{M}\_1)+Ch(\mathcal{M}\_3).$$
> 
> 
> 


An answer for algebraic D-modules would be equally useful. 


Apologies if the question is too basic. I am not a specialist. 



Additivity of characteristic cycle of holonomic D-module
Isn’t this Björk’s [**3.1.4** (p. 130)](https://books.google.com/books?id=iLnnCAAAQBAJ&pg=PA130)?


