All Questions

What is your favourite example of Gerbes? I would like to know Where do we find Gerbes in "nature"? The examples could vary from String theory to Galois theory. For example my favourite examples of ...

There is a proper map $f: X \rightarrow Y$ of projective varieties. The Decomposition Theorem of Beilinson–Bernstein–Deligne-Gabber states that $$Rf∗IC_X  \cong \oplus_a IC_{\bar{Y_a}}(L_a)[shifts]$...

For an expository piece I'm writing, it would be useful to have good examples of the following phenomenon: (1) ${\cal X}$ is a parameterized family of somethings. (Varieties, schemes, manifolds, ...