12 oct 2021 -- 14:30
Aula Tricerri, DIMaI, Firenze
Seminari di Geometria Differenziale e Analisi Complessa del Dipartimento di Matematica e Informatica "Ulisse Dini" dell'Università di Firenze
Abstract.
We will give answers to the following three questions about the set of all compact complex manifolds of a given dimension:
(i) Which linear relations between Hodge, Betti and Chern numbers are universally satisfied?
(ii) Which linear combinations of Hodge, Betti and Chern numbers are bimeromorphism invariants?
(iii) Which linear combinations of Hodge, Betti and Chern numbers are topological invariants?
We also present a strategy to answer the analogous questions when asked about `all' cohomological invariants (including e.g. the dimensions of higher pages of the Frölicher spectral sequence or Bott Chern and Aeppli cohomology). We carry this out to obtain answers in low dimensions, with answers in any dimension being reduced to specific construction problems.