Rigid compact complex surfaces that are not infinitesimally rigid

Abstract: A complex manifold is rigid if every small deformation of its complex structure is trivial. The usual argument for proving the rigidity of a complex manifold is by a well known "standard" cohomological criterium. Morrow and Kodaira posed in 1971 the problem of constructing a rigid manifold that does not satisfy it.

I will present a new criterium for rigidity of a manifold of dimension 2 that is more general than the standard one. As an application, I will produce a family of examples satisfying our criterium and not the classical one, so answering the above question.

This is a joint work with I. Bauer.

algebraic geometry

Audience: researchers in the topic

Warwick algebraic geometry seminar