An orbifold fundamental group is the fundamental group defined using charts of an orbifold, which
can retain local isotropy group information along
singular strata. For a smooth variety 
over 
that is connected, with
a smooth connected effective
Cartier divisor 
assigned positive integer
multiplicity 
, the root-orbifold group is
 |
where 
is a meridian about 
,
a small loop going once around 
in a transverse disk, joined to a
fixed basepoint in 
. The double brackets denote the normal
closure of 
.
Unlike the ordinary fundamental group of 
, this quotient can
retain a nontrivial meridian of finite order.
