I was told singular quartic algebraic surfaces in $\mathbb{P}^3\_{\mathbb{C}}$ have been completely classified and their singularities have been described.
Can anyone provide me with a resource where this classification is described, in particular the possible combination of singularities on such surfaces?


A search provided <http://www.kurims.kyoto-u.ac.jp/preprint/file/RIMS1370.pdf>, but i am wondering if there's something in one of the published books? I did not find anything in Reid - chapters on surfaces, and Beauville's book on surfaces treats only smooth surfaces.


Thanks!



Reference for the classification of (singular) degree 4 surfaces in $\mathbb{P}^3_{\mathbb{C}}$?
Look at the classical book by C. M. Jessop [*Quartic surfaces with singular points*](http://archive.org/details/cu31924062545383) (1916).


The paper by C. Segre *Etude des différentes surfaces du 4-eme ordre à conique double ou cuspidale*, Math. Ann. **24** (1884), no. 3, 313–444 is also useful. 


At any rate, I do not know if there exists a really *complete* classification.


