On CR manifolds of infinite Bloom-Graham type

08.07.2021 10:00 - 11:30

Maria Stěpanova, Moscow State University

The Bloom-Graham theorem (1977) left open the question about the form of equations for germs of real analytic manifolds of infinite type. We answer this question and give the form (reduced form) for local defining equations of manifolds of infinite type. In this case we also make the notion of Bloom-Graham type (stratified type) more exact, and this yields a rich system of new biholomorphic invariants. We will give a notion of quasimodel surfaces and prove their linear equivalence for biholomorphically equivalent manifolds.

An analogous open question was connected with the criterion of finite dimensionality for Lie algebra of infinitesimal holomorphic automorphisms. The criterion was applicable only to those manifolds which have finite type almost everywhere. We give an analogous criterion for manifolds which have infinite type everywhere.  We will also show that the set of points on the manifold where the type is fixed is semi-analytic, and at a generic point (outside a proper analytic set), the type is minimal.

Bernhard Lamel