?? "non-linear fan" .... ??? relationship to "cover" ????

??? nerve of caonical cover of toric variety ... ????.... ??? ....

?? "constructible sheaf" ... ???wrt cover ... ???? .... ?? such as forming nice AG theory .... ???? .... ????? ....

?? affine case .... ???? canonical cover of affine (?? non-/toric) variety ... toric case ... ???? certain comm ring obtained from comm monoid ... ???? ...."non-linear fan from linear" .... ??? ....

??? "cover" and "grothendieck topology" .... ???? .... ??? bit about .... ??? approximation .... small radius .... ???? ..... ???? ....