Grothendieck famously objected to the term "perverse sheaf" in Récoltes et Semailles, writing "What an idea to give such a name to a mathematical thing!  Or to any other thing or living being, except in sternness towards a person—for it is evident that of all the ‘things’ in the universe, we humans are the only ones to whom this term could ever apply.”  (Link here, in an excellent article "Comme Appelé du Néant:  The life of Alexandre Grothendieck", part 2, by Allyn Jackon.)  But a google search for '"perverse sheaf" etymology' gives only nine hits, none of which seem informative.

What is the etymology of the term "perverse sheaf"?


When MacPherson and I first started thinking about intersection homology, we realized that there was a number that measured the "badness" of a cycle with respect to a stratum.  This number had the property that when you (transversally) intersected two cycles, their 
"badness" would add. The best situation occurs for cocycles, in which case that number was zero, and the intersection of two cocycles was again a cocycle.  The worst situation was for ordinary homology, in which case that number could be as large as the codimension of the stratum.  In that case, the intersection of two cycles could even fail to be a cycle.  After a while it became clear that we needed a name for this number and we tried "degeneracy", "gap", etc., but nothing seemed to fit.  It seemed that the bad cycles were being "obstinate", but "obstinateness" did not sound reasonable.  Finally we said, "let's just call it the perversity, and we'll find a better word later". We tried again later, with no success.  (We did not realize that in some languages the word is obscene.)  When we first went to talk with Dennis Sullivan and John Morgan about these ideas, we were calling the resulting groups "perverse homology", but Sullivan suggested the alternative, "intersection homology", which seemed fine with us. This was 1974-75.  Later, when it was discovered that, for any perversity, there is an abelian category of sheaves, whose simple objects are the intersection cohomology sheaves (with that perversity) of closures of strata, Deligne coined the term "faisceaux pervers".