Up: V-filtration and spectral numbers
Previous: Milnor fibration
There is a natural action of the fundamental group
A positively oriented generator of
operates via the
monodromy operator defined by
Let be the decomposition of into the semisimple
part and the unipotent part , and set
By the monodromy theorem [1,24], the eigenvalues of
are roots of unity and .
be the decomposition of
into the generalized
eigenspaces of ,
is monodromy invariant and defines a holomorphic section in .
of rank . Note that
the direct image sheaf
is in general not finitely
generated. The Gauß-Manin connection is the regular
, the stalk of
at 0 [1,32].