Deformations of holomorphic vector bundles
and homotopy associative algebras
Volodymyr Lyubashenko
We define holomorphic vector bundles and consider the problem
of local description of deformations of holomorphic structures
for complex vector bundles.
The problem is reformulated in terms
of solutions of Maurer-Cartan differential equation.
To describe the solutions we consider a generalization of this
equation to an arbitrary strong homotopy associative algebra.
Structure theory of strong homotopy associative algebras gives
an answer to the posed question of description of deformations.