A Hodge circle associated to a rational Hodge structure 
is the image
of the unit circle under its group
homomorphism 
into the general linear group 
, where 
(Huybrechts 2016; Sutherland 2019, pp. 229,
232). On the complex vector space 
, the convention used here gives, for 
,
 |
The Hodge group is the smallest algebraic subgroup of GL(V) over 
whose real points contain this image (Huybrechts 2016). If 
whenever 
, the Hodge circle is the trivial
group.
