# Motivating derived stacks via Euclidean geometry

Here (see Section 3) triangles in Euclidean plane are used to motivate the notion of DM stack (an equilateral triangle has more symmetries than a generic triangle).

Can something similar be done to motivate derived stacks? Some sort of moduli problem in Euclidean geometry (e.g. families circles, polygons, polyhedra) where the deformation space behaves stupidly on $$\pi_0$$-level but is nice when you go full derived (and you also need to have jumping automorphism groups, since we are talking about stacks)? The derived locus should have non-empty intersection with the stacky locus (assuming this sentence even makes sense).

Don't ask me why, I just love Euclidean geometry.

• Link does not work, could you include author(s) and title please? – RP_ May 16 at 15:30
• @RP_ It says something like "In Vorbereitung - das Buch Algebraic Stacks von Kai Behrend, Brian Conrad, Dan Edidin, Barbara Fantechi, William Fulton, Lothar Göttsche und Andrew Kresch. Die folgenden Kapitelentwürfe sind für Download verfügbar." – user138661 May 16 at 15:33
• maybe this link works: math.uzh.ch/… – user138661 May 16 at 15:34
• In that case, the author and title are Kai Behrend, Introduction to Algebraic Stacks, which appeared in LMS Lecture Note Series Vol. 411. – RP_ May 16 at 15:58
• @RP_ I am not sure I agree. I have heard that they have given up on this project (and you may notice there are other authors too). Are you sure what you say is correct? Then, if I understand correctly, they have given up but Behrend persisted and published the whole thing alone? – user138661 May 16 at 16:02