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.