First variation of holomorphic forms and some applications
Consider a singular holomorphic foliation on a complex surface. Suppose \(C\) is a (possibly singular) invariant curve. One considers various local invariants, like the index and the variation of this foliation. Several formulas relating the total sum of these invariants to global invariants are (re)proved. For example, the total sum of the indices is equal to the self-intersection number of the curve \(C\). Relations with holonomy are discussed.
scientific article; zbMATH DE number 1054030