The Chern character of a complex vector bundle is the rational cohomology class obtained by summing
the exponentials of its formal Chern roots 
,
 |
The degree-zero component is the rank, and the next components are 
, 
, and 
. It is additive on exact sequences
and multiplicative on tensor products. On a smooth projective
variety it also applies to coherent sheaves
and derived-category objects through their Grothendieck classes. A real divisor twist
uses 
.
These components enter the central charges of large-volume stability conditions. Unlike a Chern class, the full Chern character is additive under direct sum.
